U.S. patent application number 12/371911 was filed with the patent office on 2009-12-03 for imaging or communications system utilizing multisample apodization and method.
Invention is credited to Drake A. Guenther, Kevin Owen, William F. Walker.
Application Number | 20090299184 12/371911 |
Document ID | / |
Family ID | 41380651 |
Filed Date | 2009-12-03 |
United States Patent
Application |
20090299184 |
Kind Code |
A1 |
Walker; William F. ; et
al. |
December 3, 2009 |
IMAGING OR COMMUNICATIONS SYSTEM UTILIZING MULTISAMPLE APODIZATION
AND METHOD
Abstract
Methods systems and system components for optimizing contrast
resolution of an imaging or sensing system utilizing multiple
channels of broadband data associated with an array of transducers.
Channels or data are filtered by passing the channels of data
through finite impulse response (FIR) filters on each channel. The
filters each have multiple taps having tap weights pre-calculated
as a function of distance of the array from an object that energy
is being transmitted to or reflected from. The weights are
pre-computed through a deterministic equation based on an a priori
system model.
Inventors: |
Walker; William F.;
(Barboursville, VA) ; Guenther; Drake A.;
(Annapolis, MD) ; Owen; Kevin; (Crozet,
VA) |
Correspondence
Address: |
LAW OFFICE OF ALAN W. CANNON
942 MESA OAK COURT
SUNNYVALE
CA
94086
US
|
Family ID: |
41380651 |
Appl. No.: |
12/371911 |
Filed: |
February 16, 2009 |
Related U.S. Patent Documents
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Application
Number |
Filing Date |
Patent Number |
|
|
61029329 |
Feb 16, 2008 |
|
|
|
61049244 |
Apr 30, 2008 |
|
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Current U.S.
Class: |
600/447 ;
382/131 |
Current CPC
Class: |
G06T 5/009 20130101;
G06T 5/002 20130101; G01S 15/8927 20130101; G01S 7/52046 20130101;
G06T 2207/20024 20130101; G10K 11/346 20130101; G06T 2207/10132
20130101 |
Class at
Publication: |
600/447 ;
382/131 |
International
Class: |
A61B 8/14 20060101
A61B008/14; G06K 9/00 20060101 G06K009/00 |
Goverment Interests
GOVERNMENT RIGHTS
[0002] This invention was made with government support under
federal grant no. 5R01EB5433 awarded by The National Institutes of
Health and U.S. Army Congressionally Directed Research Program
Grant No. W81XWH-04-1-0590. The United States Government has
certain rights in this invention.
Claims
1. A method of optimizing contrast resolution of an imaging or
sensing system utilizing multiple channels of broadband data
associated with an array of transducers, said method comprising:
filtering the channels of data by passing the channels of data
through finite impulse response (FIR) filters on each channel, the
filters each having multiple taps having tap weights pre-calculated
as a function of distance of the array from an object that energy
is being transmitted to or reflected from, said weights having been
pre-computed through a deterministic equation based on an a priori
system model; and performing one of sending the filtered channels
of data to the array or processing the filtered channels of data to
form processed data and outputting the processed data for use by a
human user.
2. The method of claim 1, wherein the deterministic equation
comprises a quadratically constrained least squares (QCLS)
algorithm that uses a cystic resolution metric.
3. The method of claim 2, wherein the quadratically constrained
least squares (QCLS) algorithm comprises a weighted quadratically
constrained least squares (WQCLS) algorithm.
4. The method of claim 1, wherein said filtering comprises
dynamically applying said tap weights.
5. The method of claim 4, wherein said dynamically applying said
tap weights varies said finite impulse response filters temporally
and spatially.
6. The method of claim 1, wherein said tap weights have varying
spatial sensitivity to distances between objects and the array.
7. The method of claim 2, wherein the quadratically constrained
least squares (QCLS) algorithm includes a value to account for an
impact of noise in the system, thereby utilizing weights that
balance the signal to noise ratio of the system with other
considerations.
8. The method of claim 1, wherein said filtering optimizes
sensitivity and contrast based on a signal-to-noise ratio versus
cystic resolution (SNR-CR) design curve.
9. The method of claim 2, wherein the quadratically constrained
least squares (QCLS) algorithm includes a spatial weighting
function that emphasizes or deemphasizes one or more predefined
locations in an instantaneous spatial response (ISR) of the
system.
10. The method of claim 1 wherein the deterministic equation
comprises a weighted quadratically constrained least squares
(WQCLS) algorithm, and wherein said filtering optimizes sensitivity
and contrast based on a signal-to-noise ratio versus cystic
resolution (SNR-CR) design curve.
11. The method of claim 1, wherein the finite impulse response
(FIR) filters each have separate I and Q channel finite impulse
response (FIR) filters
12. The method of claim 1, wherein the finite impulse response
(FIR) filters are designed to compensate for phase aberration in
the data.
13. The method of claim 1, wherein the finite impulse response
(FIR) filters are designed to compensate for amplitude aberration
in the data.
14. The method of claim 1, wherein the finite impulse response
(FIR) filters are designed to compensate for spatially distributed
aberrations in the data.
15. The method of claim 1, wherein said processing the filtered
channels of data to form processed data is performed, said
processing comprising: summing data from said taps and across said
channels to form a sample; and forming sufficient samples to
generate an image.
16. The method of claim 15, wherein said outputting comprises:
outputting the image for viewing by a human user
17. The method of claim 15, wherein said forming sufficient samples
to generate an image comprises: iterating said filtering the
channels of data and summing data to form additional samples;
forming an A-line when sufficient number of samples have been
formed; repeating said iterations said filtering the channels,
summing data and forming an A-line until a sufficient number of
A-lines have been formed to produce the image.
18. The method of claim 1, wherein the system comprises a Direct
Sampled In-phase Quadrature (DSIQ) beamformer.
19. The method of claim 1 performed on the imaging system, wherein
the imaging system is a real time imaging system.
20. A method of optimizing contrast resolution of a broadband
imaging signal received by a receive beamformer of a broadband
imaging system, the receive beamformer including multiple receive
channels, said method comprising: filtering focused receive
signals, received by the multiple channels, by passing the receive
signals through finite impulse response filters addressing multiple
receive time samples on each receive channel, said multiple time
samples being weighted according to weights pre-calculated using a
quadratically constrained least squares (QCLS) algorithm summing
outputs from said multiple time samples across said multiple
receive channels to form a sample; iterating said filtering and
summing to form additional samples; forming an A-line when
sufficient number of samples have been formed; repeating said
iterations said filtering, summing and forming an A-line until a
sufficient number of A-lines have been formed to produce an image;
and outputting the image for viewing by a human user.
21. The method of claim 20, wherein said finite impulse response
filters are depth dependent finite impulse response filters
comprising multi-tap finite impulse response filters, and wherein
weighting values of taps in said multi-tap finite impulse response
filters are varied by said system with variation in depth of an
object being imaged from an array receiving energy reflected from
the object.
22. The method of claim 20, wherein said finite impulse response
filters are depth dependent finite impulse response filters
comprising multi-tap finite impulse response filters, and wherein
said iterating includes changing tap weights of taps included in
said multi-tap impulse response filters.
23. The method of claim 20, wherein the finite impulse response
filters applied to said signals are chosen to optimize contrast
resolution of the imaging signal.
24. The method of claim 20, wherein the filter weights are
pre-calculated using a general cystic resolution metric.
25. The method of claim 20, wherein the filter weight are selected
from a look-up table storing a set of filter weights for particular
FIR apodization profiles.
26. The method of claim 20, wherein the object is located in
organic tissue.
27. The method of claim 20, wherein the object is located in living
tissue.
28. The method of claim 20 performed in vivo on an object in living
tissue.
29. The method of claim 20, wherein the broadband imaging system is
a real time imaging system.
30. The method of claim 20, wherein the beamformer comprises a
Direct Sampled In-phase Quadrature (DSIQ) beamformer.
31. A system for optimizing contrast resolution of multiple
channels of data forming a broadband signal, said system
comprising: an array of sensors electrically connected to a
plurality of channels for performing at least one of receiving and
sending the multiple channels of data; and finite impulse response
(FIR) filters connected respectively to said plurality of channels,
said finite impulse response filters each having multiple taps
adapted to apply variable tap weights pre-calculated as a function
of distance of the array from an object that energy is being
transmitted to or reflected from, said weights having been
pre-computed through a deterministic equation based on an a priori
system model.
32. The system of claim 31, wherein the deterministic equation
comprises a quadratically constrained least squares (QCLS)
algorithm that uses a cystic resolution metric.
33. The system of claim 31, further comprising a memory and a
processor, said memory being accessible by said processor; wherein
said memory stores a look-up table of sets of filter weights for
particular FIR apodization profiles, wherein a set of said filter
weights is selectable to apply to taps of said multi-tap finite
impulse response filters to change FIR apodization profiles
thereof.
34. The system of claim 31 wherein said each said tap weight is
calculated by minimizing a ratio of energy outside of a cyst being
imaged by an instantaneous spatial response calculated for the tap
for which said filter weight is being calculated, relative to the
energy inside of the cyst.
35. The system of claim 33, wherein said FIR apodization profiles
are quadratically constrained least squares FIR apodization
profiles.
36. The system of claim 33, wherein said FIR apodization profiles
are calculated using a weighted quadratically constrained least
squares (WQCLS) algorithm.
37. The system of claim 33, wherein said FIR apodization profiles
are dynamically applied and vary with distance of said array from
an object being transmitted to or received from.
38. The system of claim 33, wherein said FIR apodization profiles
are calculated to provide varying spatial sensitivity to distances
between an object and the array.
39. The system of claim 33, wherein said FIR apodization profiles
are calculated using a quadratically constrained least squares
(QCLS) algorithm including a value to account for noise in the
system, thereby balancing the signal to noise ratio of the system
with other considerations.
40. The system of claim 33, wherein said FIR apodization profiles
optimize sensitivity and contrast based on a signal-to-noise ratio
versus cystic resolution (SNR-CR) design curve.
41. The system of claim 33, wherein said FIR apodization profiles
are calculated using a quadratically constrained least squares
(QCLS) algorithm that includes a spatial weighting function that
emphasizes or deemphasizes one or more predefined locations in an
instantaneous spatial response (ISR) of the beamformer.
42. The system of claim 33, wherein said FIR apodization profiles
are calculated using a weighted quadratically constrained least
squares (WQCLS) algorithm, and wherein said filters optimize
sensitivity and contrast based on a signal-to-noise ratio versus
cystic resolution (SNR-CR) design curve.
43. The system of claim 31 wherein said finite impulse response
(FIR) filters each have separate I and Q channel finite impulse
response (FIR) filters
44. The system of claim 31 wherein the finite impulse response
(FIR) filters are designed to compensate for phase aberration in
the data.
45. The system of claim 31, wherein the finite impulse response
(FIR) filters are designed to compensate for amplitude aberration
in the data.
46. The system of claim 31, wherein the finite impulse response
(FIR) filters are designed to compensate for spatially distributed
aberrations in the data.
47. The system of claim 31, wherein said finite impulse response
(FIR) filters are applied to a Direct Sampled In-phase Quadrature
(DSIQ) beamformer.
48. The system of claim 31, wherein the system comprises a real
time sensing or imaging system.
49. A receive beamformer for optimizing contrast resolution of a
broadband imaging signal, said beamformer comprising: multiple
electrically conductive receive channels for receiving said
broadband imaging signal; and a finite impulse response filter
connected to each receive channel, each said finite impulse
response filter having multiple time samples; said multiple time
samples being weighted according to weights pre-calculated using a
quadratically constrained least squares (QCLS) algorithm.
50. The receive beamformer of claim 49, in combination with a
multi-element array electrically connected to said receive
channels, said array being configured to receive energy reflected
from an object, convert the energy to said broadband signal, and
send said broadband signal through said receive channels.
51. The receive beamformer of claim 49, further comprising a memory
and a processor, said memory being accessible by said processor;
wherein said memory stores a look-up table of sets of filter
weights for particular FIR apodization profiles, wherein a set of
said filter weights is selectable to apply to taps of said
multi-tap finite impulse response filters to change FIR apodization
profiles thereof.
52. The receive beamformer of claim 51, wherein said each said
filter weight is calculated by minimizing a ratio of energy outside
of a cyst being imaged by an instantaneous spatial response
calculated for the tap for which said filter weight is being
calculated, relative to the energy inside of the cyst.
53. The receive beamformer of claim 51, wherein said FIR
apodization profiles are quadratically constrained least squares
FIR apodization profiles.
54. The receive beamformer of claim 51, wherein said FIR
apodization profiles are calculated using a weighted quadratically
constrained least squares (WQCLS) algorithm.
55. The receive beamformer of claim 51, wherein said FIR
apodization profiles are dynamically applied and vary with distance
of said array from the object reflecting the energy.
56. The receive beamformer of claim 51, wherein said FIR
apodization profiles are calculated to provide varying spatial
sensitivity to distances between the object and the array.
57. The receive beamformer of claim 51, wherein said FIR
apodization profiles are calculated using a quadratically
constrained least squares (QCLS) algorithm including a value to
account for signal to noise ratio in the beamformer, thereby
balancing the signal to noise ratio of the beamformer with other
considerations.
58. The receive beamformer of claim 51, wherein said apodization
profiles optimize sensitivity and contrast based on a
signal-to-noise ratio versus cystic resolution (SNR-CR) design
curve.
59. The receive beamformer of claim 58, wherein said apodization
profiles are calculated using a quadratically constrained least
squares (QCLS) algorithm that includes a spatial weighting function
that emphasizes or deemphasizes one or more predefined locations in
an instantaneous spatial response (ISR) of the beamformer.
60. The receive beamformer of claim 51, wherein said apodization
profiles are calculated using a weighted quadratically constrained
least squares (WQCLS) algorithm, and wherein said filters optimize
sensitivity and contrast based on a signal-to-noise ratio versus
cystic resolution (SNR-CR) design curve.
61. The receive beamformer of claim 49, wherein said finite impulse
response (FIR) filters each have separate I and Q channel finite
impulse response (FIR) filters
62. The receive beamformer of claim 49, wherein the finite impulse
response (FIR) filters are designed to compensate for phase
aberration in the data.
63. The receive beamformer of claim 49, wherein the finite impulse
response (FIR) filters are designed to compensate for amplitude
aberration in the data.
63. The receive beamformer of claim 49, wherein said receive
beamformer comprises a Direct Sampled In-phase Quadrature (DSIQ)
beamformer.
65. A broadband imaging system comprising: a multi-element array
configured to receive energy reflected from an object, convert the
energy to a broadband signal, and output the broadband imaging
signal; a receive beamformer for optimizing contrast resolution of
an image formed from said broadband, said beamformer comprising:
multiple electrically conductive channels electrically connected to
elements of said multi-element array for receiving the broadband
signal sent by said array; a finite impulse response filter
connected to each channel, each said finite impulse response filter
having multiple time samples; a processor configured to selecting a
FIR apodization profile and apply tap weights to taps of said
finite impulse response filters; and a display for displaying an
image formed from said broadband signal.
66. The system of claim 65, further comprising: an envelope
detector configured to form A-lines generated from samples, each
said sample formed from summing outputs of said taps across said
channels.
67. The system of claim 66, further comprising a scan converter
configured to form a B-mode image from said A-lines and to output
said B-mode image to said display.
68. The system of claim 65, further comprising a transmit beam
former electrically connected to said array and configured to
control said array to transmit energy having specified
characteristics from said array.
69. The system of claim 65, wherein said system is an ultrasound
imaging system.
70. The system of claim 65, wherein said receive beamformer
comprises a Direct Sampled In-phase Quadrature (DSIQ)
beamformer.
71. A method of facilitating optimization of contrast resolution of
a broadband signal by a system, the system including multiple
channels, and finite impulse response filters having multiple taps
connected to said multiple channels, said method comprising:
storing sets of pre-calculated tap weights in computer memory, each
set of tap weights providing a tap weight for each tap of each of
said finite impulse response filters; and displaying at least one
of: at least a portion of said sets of tap weights or at least one
indicator for selecting one of said sets of tap weights.
72. The method of claim 71, wherein the tap weights are
pre-calculated by: calculating instantaneous spatial responses of
the system for each channel and each tap for an object of
predefined size and at a predetermined distance from the array;
determining tap weights that minimize energy of a combined
instantaneous spatial response reflected from locations outside of
the cyst relative to total reflected energy of the instantaneous
spatial response; and selecting the determined tap weights that
minimize the energy outside to total energy as the calculated set
of tap weights for the predefined object size and predefined
distance.
73. The method of claim 72, wherein the minimization comprises
least square minimization with a quadratic constraint.
74. A method for expanding the depth of field of an imaging system
during transmission, said method comprising: filtering channels of
data by passing the channels of data through finite impulse
response (FIR) filters having multiple taps on each channel, said
filters each having tap weights pre-calculated to simultaneously
optimize cystic point contrast across a series of cysts located at
different distances from a transducer array of the system; sending
the filtered channels of data to the array; transducing the
filtered channels of data to form energy waves; and emitting the
energy waves from the array.
75. The method of claim 74, further comprising weighting a
contribution of cysts from said series of cysts that would
otherwise have relatively more attenuated responses by the system,
when the tap weights are pre-calculated.
76. The method of claim 74, further comprising: receiving the
energy waves reflected from an object; processing the reflected
waves to form an image of the object: and displaying the image for
viewing by a human user.
Description
CROSS-REFERENCE
[0001] This application claims the benefit of U.S. Provisional
Application No. 61/029,329, filed Feb. 16, 2008, which application
is hereby incorporated herein, in its entirety, by reference
thereto. This application also claims the benefit of U.S.
Provisional Application No. 61/049,244, filed Apr. 30, 2008, which
application is hereby incorporated herein, in its entirety, by
reference thereto.
FIELD OF THE INVENTION
[0003] The present invention relates to the field of array-based
imaging and sensing, and more particularly to optimizing contrast
resolution of a beamformer used in such applications.
BACKGROUND OF THE INVENTION
[0004] The relative weighting of individual channels in an array
based imaging or sensing system can significantly, change the
sensitivity and resolution of a beamformer. FIG. 1 schematically
illustrates a prior art Delay and Sum (DAS) beamformer 1000 in
which dynamic focusing is performed by the application of time
delays 1002 to the channels of signals 1004 received from the
transducer array 2. The dynamically focused channels of signals
1006 are then weighted by scalar apodization weights 1008 ("W",
"X", and "Y", respectively in FIG. 1) and the weighted channels of
signals 1010 are then summed by a summer 1012. In medical
ultrasound imaging, the summed channel output is envelope detected
to form an "A Line," which is combined with additional A Lines to
form a B-mode image, as known in the art.
[0005] Apodization is also applied to transmit beamformers in order
to alter the beam shape, lower sidelobe levels, and improve depth
of field. Depth of field refers to the range over which the
transmitted beam is reasonably focused. Apodization on transmit can
be implemented in the most straightforward manner by simply
changing the amplitude of waveforms transmitted by different array
elements. Given that transmit circuits rarely have the ability to
arbitrarily change the amplitude of the transmit waveform, it is
often easier to implement transmit apodization by using pulse width
modulation to alter the effective power transmitted by each
element. Conventional apodization functions, like the rectangular,
Hamming, or Nuttall window, (e.g., see Nuttall, "Some Windows with
Very Good Sidelobe Behavior", IEE Trans. Acoust., Speech, and
Signal Process., col. 29. no. 1, pp. 84-91, 1981, which is hereby
incorporated herein, in its entirety, by reference thereto)
typically offer a tradeoff between the width of the main lobe of
the system spatial impulse response and the sidelobe levels (i.e.,
heights of the sidelobes). It is also notable that the selection of
these conventional apodization functions is based upon the
assumption that the imaging or sensing system is operating at a
range from the arrays that occurs in the far-field of the array.
This is almost never true for medical ultrasound imaging and is
dubious for many other applications. Thus these conventional
windows, though widely used, are known to be an imperfect solution.
Furthermore, these windows are further limited because they are
derived for a single operating frequency and modern array based
imaging and communications systems almost entirely operate in a
broad band mode.
[0006] Because receive channel weighting changes the shape of the
overall system point spread function (PSF), the particulars of the
applied apodization function greatly affect the contrast and
resolution of the final output image.
[0007] Russell, U.S. Pat. No. 4,841,492 discloses the use of
resistors to attempt to achieve a selected percent Gaussian
apodization of a focused ultrasound wavefront when transmitted from
a linear or phased array. In this case apodization is applied to
the transmit beamformer, rather than the receive beamformer.
Russell uses a siring of resistors, one resistor positioned between
the drivers of each element in the transducer array.
[0008] Lee et al. in "A hardware efficient beamformer for small
ultrasound scanners, 2005 IEEE Ultrasonics Symposium, describes a
digital receive beamformer that uses fractional delay (FD) filters
to generate delayed samples in order to reduce the complexity of
existing interpolation beamformers. Generally, FD filters are well
known in the art and have been employed successfully to enable the
application of focusing delays that are substantially smaller than
that signal sampling rate. While FD filters do improve image
quality, their design (i.e. determination of the proper degree of
sub-sample delay) must be determined empirically. Furthermore, FD
filters can only achieve image quality that is equivalent to the
use of continuously varying focal delays (i.e. no delay
quantization). The application of such continuously varying delays
will not achieve the optimal image quality (contrast and
resolution) possible for a given system.
[0009] There is a continuing need in the art for systems and
methods for optimizing the directionality, sensitivity, contrast,
and resolution of sensing, imaging, and communications systems that
use arrays of sensors (or sources). This need is particularly acute
in near-field and broadband signal applications. In the art of
medical ultrasound imaging there exists a need for improved receive
beamformers and methods for designing such beamformers to improve
image contrast, resolution, and robustness to noise and tissue
inhomogeneities.
SUMMARY OF THE INVENTION
[0010] The present invention provides methods, systems and
components for optimizing contrast resolution of an imaging or
sensing system utilizing multiple channels of broadband data
associated with an array of transducers.
[0011] A method of optimizing contrast resolution of an imaging or
sensing system utilizing multiple channels of broadband data
associated with an array of transducers is provided, including:
filtering the channels of data by passing the channels of data
through finite impulse response (FIR) filters on each channel, the
filters each having multiple taps having tap weights precalculated
as a function of distance of the array from an object that energy
is being transmitted to or reflected from, the weights having been
pre-computed through a deterministic equation based on an a priori
system model; and performing one of sending the filtered channels
of data to the array or processing the filtered channels of data to
form processed data and outputting the processed data for use by a
human user.
[0012] In at least one embodiment, the deterministic equation
comprises a quadratically constrained least squares (QCLS)
algorithm that uses a cystic resolution metric.
[0013] In at least one embodiment the quadratically constrained
least squares (QCLS) algorithm comprises a weighted quadratically
constrained least squares (WQCLS) algorithm.
[0014] In at least one embodiment, the filtering comprises
dynamically applying the tap weights.
[0015] In at least one embodiment, the dynamically application of
the tap weights varies the finite impulse response filters
temporally and spatially.
[0016] In at least one embodiment, the tap weights have varying
spatial sensitivity to distances between objects and the array.
[0017] In at least one embodiment, the quadratically constrained
least squares (QCLS) algorithm includes a value to account for an
impact of noise in the system, thereby utilizing weights that
balance the signal to noise ratio of the system with other
considerations.
[0018] In at least one embodiment, the filtering optimizes
sensitivity and contrast based on a signal-to-noise ratio versus
cystic resolution (SNR-CR) design curve.
[0019] In at least one embodiment, the quadratically constrained
least squares (QCLS) algorithm includes a spatial weighting
function that emphasizes or deemphasizes one or more predefined
locations in an instantaneous spatial response (ISR) of the
system.
[0020] In at least one embodiment, the deterministic equation
comprises a weighted quadratically constrained least squares
(WQCLS) algorithm, and wherein the filtering optimizes sensitivity
and contrast based on a signal-to-noise ratio versus cystic
resolution (SNR-CR) design curve.
[0021] In at least one embodiment, the finite impulse response
(FIR) filters each have separate I and Q channel finite impulse
response (FIR) filters.
[0022] In at least one embodiment, the finite impulse response
(FIR) filters are designed to compensate for phase aberration in
the data.
[0023] In at least one embodiment, the finite impulse response
(FIR) filters are designed to compensate for amplitude aberration
in the data.
[0024] In at least one embodiment, the finite impulse response
(FIR) filters are designed to compensate for spatially distributed
aberrations in the data.
[0025] In at least one embodiment, the processing the filtered
channels of data to form processed data is performed, the
processing comprising: summing data from the taps and across the
channels to form a sample; and forming sufficient samples to
generate an image.
[0026] In at least one embodiment, the outputting comprises:
outputting the image for viewing by a human user.
[0027] In at least one embodiment, the forming sufficient samples
to generate an image comprises: iterating the filtering the
channels of data and summing data to form additional samples
forming an A-line when sufficient number of samples have been
formed; repeating the iterations the filtering the channels,
summing data and forming an A-line until a sufficient number of
A-lines have been formed to produce the image.
[0028] In at least one embodiment, the system comprises a Direct
Sampled In-phase Quadrature (DSIQ) beamformer.
[0029] In at least one embodiment, the method is performed on the
imaging system, wherein the imaging system is a real time imaging
system.
[0030] A method of optimizing contrast resolution of a broadband
imaging signal received by a receive beamformer of a broadband
imaging system, the receive beamformer including multiple receive
channels is provided, wherein the method includes: filtering
focused receive signals, received by the multiple channels, by
passing the receive signals through finite impulse response filters
addressing multiple receive time samples on each receive channel,
the multiple time samples being weighted according to weights
pre-calculated using a quadratically constrained least squares
(QCLS) algorithm; summing outputs from the multiple time samples
across the multiple receive channels to form a sample; iterating
the filtering and summing to form additional samples; forming an
A-line when sufficient number of samples have been formed;
repeating the iterations the filtering, summing and forming an
A-line until a sufficient number of A-lines have been formed to
produce an image; and outputting the image for viewing by a human
user.
[0031] In at least one embodiment, the finite impulse response
filters are depth dependent finite impulse response filters
comprising multi-tap finite impulse response filters, and wherein
weighting values of taps in the multi-tap finite impulse response
filters are varied by the system with variation in depth of an
object being imaged from an array receiving energy reflected from
the object.
[0032] In at least one embodiment, the finite impulse response
filters are depth dependent finite impulse response filters
comprising multi-tap finite impulse response filters, and wherein
the iterating includes changing tap weights of taps included in the
multi-tap impulse response filters.
[0033] In at least one embodiment, the finite impulse response
filters applied to the signals are chosen to optimize contrast
resolution of the imaging signal.
[0034] In at least one embodiment, the filter Weights are
pre-calculated using a general cystic resolution metric.
[0035] In at least one embodiment, the filter weights are selected
from a look-up table storing a set of filter weights for particular
FIR apodization profiles.
[0036] In at least one embodiment, the object is located in organic
tissue.
[0037] In at least one embodiment, the object is located in living
tissue.
[0038] In at least one embodiment, the method is performed in vivo
on an object in living tissue.
[0039] In at least one embodiment, the broadband imaging system is
a real time imaging system.
[0040] In at least one embodiment, the beamformer comprises a
Direct Sampled In-phase Quadrature (DSIQ) beamformer.
[0041] A system for optimizing contrast resolution of multiple
channels of data forming a broadband signal is provided, wherein
the system includes: an arrays of sensors electrically connected to
a plurality of channels for performing at least one of receiving
and sending the multiple channels of data; and finite impulse
response (FIR) filters connected respectively to the plurality, of
channels, the finite impulse response filters each having multiple
taps adapted to apply variable tap weights pre-calculated as a
function of distance of the array from an object that energy is
being transmitted to or reflected from, the weights having been
pre-computed through a deterministic equation based on an a priori
system model.
[0042] In at least one embodiment, the deterministic equation
comprises a quadratically constrained least squares (QCLS)
algorithm that uses a cystic resolution metric.
[0043] In at least one embodiment, the system includes a memory and
a processor, the memory being accessible by the processor; wherein
the memory stores a look-up table of sets of filter weights for
particular FIR apodization profiles, wherein a set of the filter
weights is selectable to apply to taps of the multi-tap finite
impulse response filters to change FIR apodization profiles
thereof.
[0044] In at least one embodiment, each tap weight is calculated by
minimizing a ratio of energy outside of a cyst being imaged by an
instantaneous spatial response calculated for the tap for which the
filter weight is being calculated, relative to the energy inside of
the cyst.
[0045] In at least one embodiment, the FIR apodization profiles are
quadratically constrained least squares FIR apodization
profiles.
[0046] In at least one embodiment, the FIR apodization profiles are
calculated using a weighted quadratically constrained least squares
(WQCLS) algorithm.
[0047] In at least one embodiment, the FIR apodization profiles are
dynamically applied and vary with distance of the array from an
object being transmitted to or received from.
[0048] In at least one embodiment, the FIR apodization profiles are
calculated to provide varying spatial sensitivity to distances
between an object and the array.
[0049] In at least one embodiment, the FIR apodization profiles are
calculated using a quadratically constrained least squares (QCLS)
algorithm including a value to account for noise in the system,
thereby balancing the signal to noise ratio of the system with
other considerations.
[0050] In at least one embodiment, the FIR apodization profiles
optimize sensitivity and contrast based on a signal-to-noise ratio
versus cystic resolution (SNR-CR) design curve.
[0051] In at least one embodiment, the FIR apodization profiles are
calculated using a quadratically constrained least squares (QCLS)
algorithm that includes a spatial weighting function that
emphasizes or deemphasizes one or more predefined locations in an
instantaneous spatial response (ISR) of the beamformer.
[0052] In at least one embodiment, the FIR apodization profiles are
calculated using a weighted quadratically constrained least squares
(WQCLS) algorithm, and wherein the filters optimize sensitivity and
contrast based on a signal-to-noise ratio versus cystic resolution
(SNR-CR) design curve.
[0053] In at least one embodiment, the finite impulse response
(FIR) filters each have separate I and Q channel finite impulse
response (FIR) filters.
[0054] In at least one embodiment, the finite impulse response
(FIR) filters are designed to compensate for phase aberration in
the data.
[0055] In at least one embodiment, the finite impulse response
(FIR) filters are designed to compensate for amplitude aberration
in the data.
[0056] In at least one embodiment, the finite impulse response
(FIR) filters are designed to compensate for spatially distributed
aberrations in the data.
[0057] In at least one embodiment, the finite impulse response
(FIR) filters are applied to a Direct Sampled In-phase Quadrature
(DSIQ) beamformer.
[0058] In at least one embodiment, the system comprises a real time
sensing or imaging system.
[0059] A receive beamformer for optimizing contrast resolution of a
broadband imaging signal is provided, including: multiple
electrically conductive receive channels for receiving the
broadband imaging signal; and a finite impulse response filter
connected to each receive channel, each the finite impulse response
filter having multiple time samples; the multiple time samples
being weighted according to weights pre-calculated using a
quadratically constrained least squares (QCLS) algorithm.
[0060] In at least one embodiment, the receive beamformer is
provided in combination with a multi-element array electrically
connected to the receive channels, the arrays being configured to
receive energy reflected from an object, convert the energy to the
broadband signal, and send the broadband signal through the receive
channels.
[0061] In at least one embodiment, the beamformer includes a memory
and a processor, the memory being accessible by the processor;
wherein the memory stores a look-up table of sets of filter weights
for particular FIR apodization profiles, wherein a set of the
filter weights is selectable to apply to taps of the multi-tap
finite impulse response filters to change FIR apodization profiles
thereof.
[0062] In at least one embodiment, each filter weight is calculated
by minimizing a ratio of energy outside of a cyst being imaged by
an instantaneous spatial response calculated for the tap for which
the filter weight is being calculated, relative to the energy
inside of the cyst.
[0063] In at least one embodiment, the FIR apodization profiles are
quadratically constrained least squares FIR apodization
profiles.
[0064] In at least one embodiment, the FIR apodization profiles are
calculated using a weighted quadratically constrained least squares
(WQCLS) algorithm.
[0065] In at least one embodiment, the FIR apodization profiles are
dynamically applied and vary with distance of the array from the
object reflecting the energy.
[0066] In at least one embodiment, the FIR apodization profiles are
calculated to provide varying spatial sensitivity to distances
between the object and the array.
[0067] In at least one embodiment, the FIR apodization profiles are
calculated using a quadratically constrained least squares (QCLS)
algorithm including a value to account for signal to noise ratio in
the beamformer, thereby balancing the signal to noise ratio of the
beamformer with other considerations.
[0068] In at least one embodiment, the apodization profiles
optimize sensitivity and contrast based on a signal-to-noise ratio
versus cystic resolution (SNR-CR) design curve.
[0069] In at least one embodiment, the apodization profiles are
calculated using a quadratically constrained least squares (QCLS)
algorithm that includes a spatial weighting function that
emphasizes or deemphasizes one or more predefined locations in an
instantaneous spatial response (ISR) of the beamformer.
[0070] In at least one embodiment, the apodization profiles are
calculated using a weighted quadratically constrained least squares
(WQCLS) algorithm, and wherein the filters optimize sensitivity and
contrast based on a signal-to-noise ratio versus caustic resolution
(SNR-CR) design curve.
[0071] In at least one embodiment, the finite impulse response
(FIR) filters each have separate I and Q channel finite impulse
response (FIR) filters.
[0072] In at least one embodiment, the finite impulse response
(FIR) filters are designed to compensate for phase aberration in
the data.
[0073] In at least one embodiment, the Finite impulse response
(FIR) filters are designed to compensate for amplitude aberration
in the data.
[0074] In at least one embodiment, the receive beamformer comprises
a Direct Sampled In-phase Quadrature (DSIQ) beamformer.
[0075] A broadband imaging system is provided that includes: a
multi-element array configured to receive energy reflected from an
object, convert the energy to a broadband signal, and output the
broadband imaging signal; a receive beamformer for optimizing
contrast resolution of an image formed from the broadband, the
beamformer comprising: multiple electrically conductive channels
electrically connected to elements of the multi-element array for
receiving the broadband signal sent by the array; a finite impulse
response filter connected to each channel, each the finite impulse
response filter having multiple time samples; a processor
configured to selecting a FIR apodization profile and apply lap
weights to taps of the finite impulse response filters; and a
display for displaying an image formed from the broadband
signal.
[0076] In at least one embodiment, the system includes an envelope
detector configured to form A-lines generated from samples, each
the sample formed from summing outputs of the taps across the
channels.
[0077] In at least one embodiment, the system further includes a
scan converter configured to form a B-mode image from the A-lines
and to output the B-mode image to the display.
[0078] In at least one embodiment, the system further includes a
transmit beamformer electrically connected to the array and
configured to control the array to transmit energy having specified
characteristics from the array.
[0079] In at least one embodiment, the system is an ultrasound
imaging system.
[0080] In at least one embodiment, the system includes a Direct
Sampled In-phase Quadrature (DSIQ) beamformer.
[0081] A method of facilitating optimization of contrast resolution
of a broadband signal by a system, the system including multiple
channels, and finite impulse response filters having multiple taps
connected to the multiple channels is provided, including: storing
sets of pre-calculated tap weights in computer memory, each set of
lap weights providing a tap weight for each lap of each of the
finite impulse response filters; and displaying at least one of: at
least a portion of the sets of tap weights or at least one
indicator for selecting one of the sets of tap weights.
[0082] In at least one embodiment, the tap weights are
pre-calculated by: calculating instantaneous spatial responses of
the system for each channel and each tap for an object of
predefined size and at a predefined distance from the array;
determining tap weights that minimize energy of a combined
instantaneous spatial response reflected from locations outside of
the cyst relative to total reflected energy of the instantaneous
spatial response; and selecting the determined tap weights that
minimize the energy outside to total energy as the calculated set
of tap weights for the predefined object size and predefined
distance.
[0083] In at least one embodiment, the minimization comprises least
square minimization with a quadratic constraint.
[0084] A method for expanding the depth of field of an imaging
system during transmission is provided, wherein the method
includes: filtering channels of data by passing the channels of
data through finite impulse response (FIR) filters having multiple
taps on each channel, the filters each having tap weights
pre-calculated to simultaneously optimize cystic point contrast
across a series of cysts located at different distances from a
transducer array of the system; sending the filtered channels of
data to the array; transducing the filtered channels of data to
form energy waves; and emitting the energy waves from the
array.
[0085] In at least one embodiment, the method further includes
weighting a contribution of cysts from the series of cysts that
would otherwise have relatively more attenuated responses by the
system, when the tap weights are pre-calculated.
[0086] In at least one embodiment, the method further includes:
receiving the energy waves reflected from an object; processing the
reflected waves to form an image of the object; and displaying the
image for viewing by a human user.
[0087] These and other features of the invention will become
apparent to those persons skilled in the art upon reading the
details of the systems, components and methods as more fully
described below.
BRIEF DESCRIPTION OF THE DRAWINGS
[0088] FIG. 1 is a schematic illustration of a prior art delay and
sum (DAS) beamformer.
[0089] FIG. 2 is a schematic illustration of a receive beamformer
according to the present invention.
[0090] FIG. 3 is a schematic illustration of a system according to
the present invention.
[0091] FIG. 4 illustrates events that may be performed in a method
of applying dynamic receive apodization to a broadband imaging
signal according to an embodiment of the present invention.
[0092] FIG. 5 is a schematic illustration of a user interface
according to an embodiment or the present invention, including a
display upon which images generated by processing according to the
present invention are displayable.
[0093] FIG. 6 illustrates a table of tap weights having been
pre-calculated for a cyst radius of about 0.3 mm at various
distances for a multiplicity of taps and channels.
[0094] FIGS. 7A-7I highlight how the GCR metric can be used to
design beamformers.
[0095] FIG. 8 illustrates a typical computer system, all or a
portion of which may be incorporated into a system according to an
embodiment of the present invention.
[0096] FIG. 9 is a schematic illustration of a prior art complex
beamformer.
[0097] FIG. 10 is a schematic illustration of a complex beamformer
according to the present invention.
[0098] FIG. 11 shows cystic point contrast curves for a 5-tap FIR
beamformer according to an embodiment of the present invention.
[0099] FIG. 12 shows cystic point contrast curves for a prior art
beamformer and for an embodiment of a beamformer according to the
present invention.
[0100] FIGS. 13A-13C show integrated lateral beamplots, FIGS.
3D-13F show plots of cystic contrast vs. cyst size, and FIGS.
13G-13I show plots of cystic contrast vs. receive channel signal to
noise ratio (SNR) cures comparing different apodization functions
at different dynamic receive focal depths (1.0 cm, 2.0 cm and 3.0
cm, respectively, with transmission (Tx) focus fixed at 2.0
cm).
[0101] FIG. 14 shows calculated FIR-QCLS weights for data
dynamically focused at 2.0 cm according to an embodiment of the
present invention.
[0102] FIG. 15 shows the magnitude and phase responses for 3-tap,
5-tap and 7-tap FIR filters represented in FIG. 14.
[0103] FIGS. 16A-16N show unaberrated and aberrated simulation
instantaneous spatial responses (ISRs) for different apodization
functions.
[0104] FIG. 16O shows the phase aberration profile used to achieve
the results shown in FIGS. 16A-16N.
[0105] FIG. 17 shows plots of unaberrated and aberrated cystic
point contrast curves for rectangular and 7-tap ISRs in the absence
of noise.
[0106] FIGS. 18A-18C show plots of the mean cystic contrast for
various aberrated ISRs relative to that formed when using a
rectangular window function.
[0107] FIG. 19 shows log compressed, envelope detected experimental
ISRs.
[0108] FIGS. 20A-20C show experimental integrated lateral beamplots
and GCR metric curves.
[0109] FIG. 21 shows QCLS weights for multi-tap FIR filters
according to an embodiment of the present invention.
[0110] FIG. 22 shows magnitude and phase responses for the 3-tap,
5-tap and 7-tap FIR filters the weight of which are represented in
FIG. 21.
[0111] FIGS. 23A-23E show images of simulated B-mode images of a
cyst, using various apodization schemes.
[0112] FIG. 23F is a representation of the size of the chest used
for the images of FIGS. 21A-21E23A-23E.
[0113] FIGS. 24A-24B plot cyst CNR curves computed from equation
(11) as a function of cyst radius.
[0114] FIGS. 25A-25D show schematic representation of various
beamformers, results from which are compared in some of the
examples herein.
[0115] FIGS. 26A-26B show design SNR-CR curves for a DF-FIR
beamformer according to the present invention, as well as the CR
performance of a rectangular apodized DAS beamformer, and SMF
beamformer, and five different 9-tap DF-FIR beamformers.
[0116] FIGS. 27A-27B show design SNR-CR curves for a GF-FIR
beamformer according to the present invention as well as the CR
performance of a rectangular apodized DAS beamformer, an SMF
beamformer, and three different 9-tap GF-FIR beamformers.
[0117] FIG. 28 shows integrated lateral beamplots for various
beamformers to illustrate how the sensitivity constrained QCLS
algorithm according to the present invention affects the ISR's of a
FIR beamformer.
[0118] FIG. 29A shows integrated lateral beamplots for a
rectangular apodized DAS beamformer, an SMF beamformer, and a 9-tap
DF-FIR beamformer as the weighting term assigned to ISR energy
further away from the focus increases (N=0, N=1, and N=2),
respectively.
[0119] FIG. 29B shows cystic resolution curves as a function of
cyst radius for the beamformers referred to in FIG. 29A.
[0120] FIG. 29C shows the CR performance as a function of channel
SNR for the five beamformers referred to in FIGS. 29A-29B,
respectively.
[0121] FIGS. 30A-30C show results of aberration simulations using
three operating points for a 7-tap DF-FIR beamformer according to
the present invention.
[0122] FIGS. 31A-31C show results of aberration simulations using
three operating points for a 7-tap DF-FIR beamformer using
WQCLS-FIR filters according to the present invention.
[0123] FIG. 32 shoots integrated lateral beamplots for a
conventional DSIQ beamformer and a DSIQ beamformer according to
embodiments of the present invention.
DETAILED DESCRIPTION OF THE INVENTION
[0124] Before the present systems, methods and computer readable
storage media are described, it is to be understood that this
invention is not limited to particular embodiments described, as
such may, of course, vary. It is also to be understood that the
terminology used herein is for the purpose of describing particular
embodiments only, and is not intended to be limiting, since the
scope of the present invention will be limited only by the appended
claims.
[0125] Where a range of values is provided, it is understood that
each intervening value, to the tenth of the unit of the lower limit
unless the context clearly dictates otherwise, between the upper
and lower limits of that range is also specifically disclosed. Each
smaller range between any stated value or intervening value in a
stated range and any other stated or intervening value in that
stated range is encompassed within the invention. The upper and
lower limits of these smaller ranges may independently be included
or excluded in the range, and each range where either, neither or
both limits are included in the smaller ranges is also encompassed
within the invention, subject to any specifically excluded limit in
the stated range. Where the stated range includes one or both of
the limits, ranges excluding either or both of those included
limits are also included in the invention.
[0126] Unless defined otherwise, all technical and scientific terms
used herein have the same meaning as commonly understood by one of
ordinary skill in the art to which this invention belongs. Although
any methods and materials similar or equivalent to those described
herein can be used in the practice or testing of the present
invention, the preferred methods and materials are now described.
All publications mentioned herein are incorporated herein by
reference to disclose and describe the methods and/or materials in
connection with which the publications are cited.
[0127] It must be noted that as used herein and in the appended
claims, the singular forms "a", "an", and "the" include plural
referents unless the context clearly dictates otherwise. Thus, for
example, reference to "a tap" includes a plurality of such taps and
reference to "the signal" includes reference to one or more signals
and equivalents thereof known to those skilled in the art, and so
forth.
[0128] Throughout this disclosure the superscript "T" is intended
to indicate a matrix or vector transpose operation. In cases where
the matrix or vector of interest is complex rather than simply real
it should be understood that the Hermitian or Complex Transpose
should be applied.
[0129] The publications discussed herein are provided solely for
their disclosure prior to the filing date of the present
application. Nothing herein is to be construed as an admission that
the present invention is not entitled to antedate such publication
by virtue of prior invention. Further, the dates of publication
provided may be different from the actual publication dates which
may need to be independently confirmed. Further, all references
identified herein, including non-patent literature, patents, patent
applications and patent application publications are incorporated
herein, in their entireties, by reference thereto.
DEFINITIONS
[0130] The terms "f-number" and "f/#", as used herein, refer to the
range of interest (often the focal length) divided by the linear
dimension of the aperture over which data is collected (receive
aperture) or transmitted (transmit aperture). The transmit aperture
is the width of the number of simultaneous firing transducer
elements in the array of the system used to transmit the beam that
caused the returning wave to be reflected off of an object. The
above definition is to typically referred to as the lateral
f-number, recognizing that most modern imaging systems utilize
linear or phased arrays that have a diversity of elements in only
one dimension. For such systems one of ordinary skill in the art
will also recognize the elevation f-number which simply refers to
the range of interest divided by the elevation dimension of the
array. Two-dimensional transducer arrays are now becoming common
and for these systems lateral and elevation f-number have their
clear meaning, with the difference being that such arrays have a
plurality of elements in both the lateral and elevation dimensions.
Lateral resolution is typically best (smallest), where there is a
large aperture, short focal length, and short wavelength. In terms
of f-number, resolution is best (finest) when the f-number is low
and the wavelength is short.
[0131] The "point spread function" or "PSF" describes the response
of an imaging system to a point source or object. Generically, the
PSF refers to the system response over a combination of temporal
and spatial dimensions. The specific combination of temporal and
spatial dimensions much be determined from context, although in
some cases the term may be used generically to refer to the system
response to a point target.
[0132] "Apodization" refers to the act of reducing side lobes that
occur in the point spread function.
[0133] An "apodization profile" refers to the amplitude weighting
function applied across the transmit or receive aperture. Typical
apodization functions are Gaussian, Hamming, or Rectangular window
functions. In systems operating on complex data the apodization
function may include a phase perturbation in addition to the
amplitude weighting. Such phase perturbations are particularly
useful for spreading the focus of a transmit beam over a larger
range. In receive mode the apodization function is typically
dynamically adjusted with range to maintain a constant f-number and
thus constant speckle size.
[0134] "Cystic resolution" refers to a metric that can be used to
characterize the resolution of arbitrary broadband coherent imaging
systems. Conceptually, caustic resolution describes the achieved
contrast for a perfect anechoic cyst of a given diameter. Such
measures can be considered over a range of cyst diameters to form a
cystic resolution curve. This metric is described in detail in
Ranganathan et al., "Cystic Resolution: A Performance Metric for
Ultrasound Imaging Systems", IEEE Transactions on Ultrasonics,
Ferroelectrics and Frequency Control, Vol. 54, No. 4, April 2007,
which is hereby incorporated herein, in its entirety, by reference
thereto. A more broadly defined version of this metric is described
in detail in Guenther, D. A. and W. F. Walker, "Generalized Cystic
Resolution: A Metric for Assessing the Fundamental Limits on
Beamformer Performance," IEEE Transactions on Ultrasonics,
Ferroelectrics, and Frequency Control, vol. 56, no. 1, pp. 77-90,
2009, which is also incorporated herein, in its entirety, by
reference thereto.
[0135] "Contrast resolution" is a general term describing the
contrast of targets in an image. "Cystic resolution" is a specific
term which can be stated mathematically and is representative of
contrast resolution. Technically, the present invention is aimed at
optimizing the "cystic resolution" of the imaging system so by
default it improves the contrast resolution.
[0136] A "finite impulse response filter" or "FIR filter" is a type
of a digital filter. The impulse response, the filter's response to
a Kronecker delta input, is finite because it settles to zero in a
finite number of sample intervals. This is in contrast to infinite
impulse response filters which have internal feedback and may
continue to respond indefinitely. The impulse response of an Nth
order FIR filter lasts for N+1 samples, and then dies to zero.
[0137] A FIR filter includes a delay line, so at sample time "n"
access to samples n-1, n-2, n-3, . . . are available, for as many
prior samples as needed. A "tap", as used herein refers to any
point in the delay line where the FIR filter uses the data. The
number of taps of a FIR filter is typically the number of delays
plus one, e.g., a four tap filter would use sample n, sample n-1,
sample n-2 and sample n-3. The difference equation which defines
how the input signal to the FIR filter is related to the output
signal from the FIR filter is defined by:
y[n]=b.sub.0x[n]+b.sub.1x[n-1]+ . . . +b.sub.Nx[n-N] (1)
where x[n] is the input signal, y[n] is the output signal and
b.sub.i are the filter coefficients. N is known as the filter
order; an N.sup.th-order filter has (N+1) terms on the right-hand
side; these are commonly referred to as taps.
DETAILED DESCRIPTION
[0138] The present invention provides methods for focusing data
with an array of sensors, as well as systems and components for
performing such methods. Examples of uses of methods described
herein include, but are not limited to use in: a receive ultrasound
beamformer, a transmit ultrasound beamformer, reception of acoustic
data from an array of microphones, reception of data from an array
of seismic sensors, such as used in oil exploration, reception
and/or transmitting using an array of radio antennas, such as for
communications or radio astronomy, etc.
[0139] FIG. 2 is a schematic representation of a receive beamformer
10 according to the present invention. Like the prior art
beamformer 1000 of FIG. 1, beamformer 10 applies apodization after
the dynamic focal delays 12 have been applied. Rather than applying
scalar apodization weights to the delayed channels 16 however, the
present invention uses FIR filters 18 to apply the apodization.
Note that only three FIR filters 18 are presented in FIG. 2 for
simplicity and clarity. In reality, there should be five FIR
filters 18 in the example of FIG. 2, as each delay line 16 has a
FIR filter 18 applied thereto. The FIR Filters of FIG. 2 not only
mimic the function of conventional apodization sleights, but also
apply frequency dependent weights and phase delays. It is this
capability that accounts for the improved performance of the FIR
apodization beamformer.
[0140] Also, it is noted that the beamformer 10 can be used for
receive only systems that do not employ a transmit beamformer, or
can be used equally as well in systems that do include a transmit
beamformer 1 as represented in phantom lines in FIG. 2. For
example, some passive SONAR systems employ receive only beamforming
to enable rapid tracking and avoid enemy detection, and
opto-acoustic imaging devices use the ultrasound transducer purely
as a receiver. As noted, the present beamforming architecture and
methods can be readily applied to these systems, and offers the
potential to significantly improve point resolution and contrast of
the output images.
[0141] It should also be noted that the FIR apodization method
described herein is also directly applicable to a transmit
beamformer, either operating alone or as a part of a
transmit-receive system. While channel varying transmit waveforms
are known in the prior-art, notably the frequency dependent
focusing method described by Hossack et. al. (U.S. Pat. No.
6,108,273), by J. A. Hossack et. al., "Extended focal depth imaging
for medical ultrasound" in Proceedings of the 1996 IEEE Ultrasonics
Symposium, p. 1535-40. and "Dynamic-transmit focusing using
time-dependent focal zone and center frequency" by Zhou and Hossack
in IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency
Control February 2003, p. 142-52) and the minimum sum squared error
beamformer of Ranganathan et. al. (Ranganathan, K. and W. F.
Walker. "A Novel Beamformer Design Method for Medical Ultrasound:
Part I: Theory," IEEE Trans. Ultrason. Ferroelec. Freq. Contr.,
IEEE Trans. Ultrason. Ferroelec. Freq. Contr, vol. 50, no. 1, pp.
15-24, January 2003. and Ranganathan, K. and W. F. Walker, "A Novel
Beamformer Design Method for Medical Ultrasound: Part II:
Simulation Results," IEEE Trans. Ultrason. Ferroelec. Freq. Contr.,
vol. 50, no. 1, pp. 25-39, January 2003), these methods are more
difficult to implement in hardware and do not achieve the same
level of improvement as the methods described herein. In order to
optimize the apodization weights 20.sub.1, 20.sub.2, . . . ,
20.sub.x applied by beamformer 10 to optimize contrast resolution,
the present invention provides methods for calculating optimal
weights 20.sub.1, 20.sub.2, . . . , 20.sub.x that are applied in
the FIR filters 18. The time delays applied in the example shown in
FIG. 2 are all equal across the FIR filter and between all the
channels, but need not be. By using different time delays among the
channels, it is possible to further increase performance, but
possibly at the cost of increased system complexity. Varying delays
between channels are of course already applied through dynamic
receive focusing, so in such cases the additional complexity would
occur in the design phase but not necessarily in implementation.
The delay s within the FIR filter bank may also be varying between
the different taps. One likely application of such variation would
be in applying the present invention to the Direct Sampled In
Phase--Quadrature beamformer ("Ultrasonic Imaging Beam-former
Apparatus and Method," T. N. Blalock, W. F. Walker, and J. A.
Hossack. PCT Application filed Jan. 14, 2004, U.S. patent
application Ser. No. 11/160,915 and Ranganathan, K., M. K. Santy,
T. N. Blalock. J. A. Hossack, and W. F. Walker, "Direct Sampled IQ
Beamforming for Compact and Very Low Cost Ultrasound Beamforming,"
IEEE Trans. Ultrason. Ferroelec. Freq. Contr., vol. 51, no. 9, pp.
1082-94, September 2004.)..)..), both of which are hereby
incorporated, herein, in their entireties, by reference thereto.
After applying the apodization weights 20.sub.1, 20.sub.2, . . . ,
20.sub.x via taps 20T (note that five-tap FIR filters 18 are shown
in FIG. 2, but the number of taps may vary), the filtered channels
of signals 22 are then summed by a summer 24. The summed channel
output at a particular instant in time is a single sample of a
summed RF line. Successive time samples from the summer form a
complete summed RF line. After applying the apodization weights
20.sub.1, 20.sub.2, . . . , 20.sub.x via taps 20T (note that
five-tap FIR filters 18 are shown in FIG. 2, but the number of taps
may vary), the filtered channels of signals 22 are then summed by a
summer 24. The summed channel is output as summed RF line. In a
tropical embodiment this summed RF line is streamed continuously
into an envelope detector 40 and is output continuously as a single
"A-Line." A-Lines are processed/combined by scan converter 45 to
form a B-mode image, which can be displayed for viewing by a human
user. Alternatively, the summed RF lines may be processed to
measure blood velocity or tissue motion, to estimate tissue
properties using any of a broad range of techniques known as tissue
characterization, to measure tissue displacements or strains for
tissue elasticity estimation, or for any of a number of other
methods well known to those of skill in the art.
[0142] The present invention provides a beamformer configured to
dynamically apply receive aperture weights using spatially and
temporally variant finite impulse response (FIR) filters 18. In
general, the FIR filters 18 on each channel are unique for every
spatial point in the output image (which is formed from the A lines
combined into a B-mode image). In one simple embodiment, the
present invention provides a linear arrays 2 without beamsteering,
where the receive FIR filters 18 vary only with depth (i.e.
distance from the object that an image is being constructed of).
The filter weights 20.sub.1, 20.sub.2, . . . , 20.sub.x are
calculated to maximize contrast resolution.
[0143] FIG. 3 is a basic, schematic representation of an ultrasound
system 100 according to one embodiment of the present invention
that is referred to in order to generally describe the operations
of an ultrasound system to produce an image of an object 3. System
100 may optionally include a transmit beamformer, which may include
input thereto bit controller 30 to send electrical instructions to
array 2 as to the specifics of the ultrasonic waves to be emitted
by array 2. Alternatively, system 100 may be a receive only system
and the emitted waves may be directed to the object 3 from an
external source.
[0144] In either case, waves 4 reflected by the object 3 (and
surrounding environment) are received by array 2 and converted to
radio frequency (RF) signals 14 that are input to receive
beamformer 10. Controller 30 may be external of the beamformer 10,
as shown, or integrated therewith and may be directed by a user to
select a set of tap weights based on a particular cast size that
the tap weights have been calculated for. In one embodiment the
user directly selects the cyst size of interest, while in another
realization the user may select the cyst size indirectly by trading
spatial resolution for image contrast. In many applications the
desired cyst size may be selected by default based on trials
performed by the system designers. Additionally, controller 30
automatically and dynamically changes sets of tap weights used in
the FIR filters 18 of receive beam former 10 as the distance
between the array 2 and object 3 changes, as described in more
detail below. Thus the time delays change as a function of
distance, and accordingly, the FIR tap weights will also change as
a function of distance. The tap weights may be updated as
frequently as every sample taken by the system but do not
necessarily need to be updated this frequently, since they do not
change that rapidly with distance Distance/depth is typically
calculated assuming a constant speed of sound in tissue (i.e. 1540
m/s) and then time of flight is recorded such that the returning
echoes have a known origination. Thus, system 100 also stores in
memory (either memory integrated into controller 30 or beamformer
10, or connected thereto for ready access) a look up table that
contains sets of tap weights useable in the FIR filters 18, wherein
the tap weight sets vary according to cyst size, as well as
distance of the array 2 from the cyst. Tap weights will also vary
depending on system characteristics such as aperture size, transmit
frequency, bandwidth, and other parameters that affect the system's
ISR. The summed RF lines output by the receive beamformer are input
to an envelope detection module, which may be separate from and
controlled by, or incorporated in controller 30. Envelope detected
A-Lines are output from the detection module 40 and input into a
scan converter module 45. The scan converter 45 processes data from
multiple A-Lines to determine the data to be output at each image
pixel. The B-mode image formed within the scan converter 45 is
displayed on display 50.
[0145] The apodization applied by beamformer 10 is data independent
and the filter tap weights 20.sub.1, 20.sub.2, . . . , 20.sub.x are
deterministic given the a priori system model. The FIR filter
weights (i.e., tap weights) are computed through a deterministic
equation (the QCLS algorithm) as described herein, which requires
system modeling and characterization (the "a priori system model.")
Beamformer 10 maximizes contrast resolution using a constrained
least squares design algorithm that incorporates a general cystic
resolution metric, which implicitly controls the mainlobe size of
the resultant spatial point spread function (PSF). Notably the
system"), which may include one or more of the system's ISR must be
characterized for the imaging conditions under which the FIR
filters are to be employed. This characterization may be performed
using computer simulations, experimental measurement, analytical
theory, or some combination of the three. In addition, the required
characterization may be extrapolated from known conditions to save
the time required to fully characterize each condition. In some
circumstances, such as designing FIR filter weights to extend the
depth of field of a transmit beamformer, it may be necessary to
consider ISRs at a number of ranges and time points. In a related
design problem the system designer might combine ISRs for a number
of possible phase aberration profiles and then design the FIR
filter weights that would optimize cystic contrast over that set of
possible aberrations. Other variations of the present invention are
possible. For instance, utilizing the baseband or envelope
representation of the ISR may be necessary in order to implement
complex FIR weights or use the FIR beamformer with baseband I/Q
data. In other circumstances, utilizing ISRs with different system
parameters (transmit frequency, transmit focus, fractional
bandwidth) in order to design for FIR filter weights that are
optimal over a range of operating parameters and conditions,
complex information, envelope data, multiple ISRs, multiple
instances of the same ISR, noise statistics, SNR, cyst size,
etc.
[0146] The filter tap weight calculations are not limited by
nearfield, narrowband assumptions and do not require estimation of
the receive signal second order statistics. This is an important
contrast with so-called adaptive beamformers (e.g., Frost
Beamformer, Capon Beamformer, etc.) that adjust their operation and
freights depending upon the data input to the beamformer. Thus the
present invention avoids the need for extensive computation and
adaptive adjustment or the adaptive beamformers and is thus more
suited to cost efficient implementation.
[0147] Beamformer 10 can be readily adapted to existing commercial
architectures and previously described architectures including, but
not limited to those described in U.S. Patent Application
Publication No. 2007/0016022.
[0148] The present invention offers the potential to significantly
improve the point resolution and contrast of one-way beamforming
systems, including, but not limited to passive ultrasound systems.
The present invention is further applicable to improve performance
of the so-called, spatial matched filter beamformer, e.g., see Kim
et al., "Efficient array beam forming by spatial filtering for
ultrasound B-mode imaging", Journal of the Acoustic Society of
America, vol. 120, pp. 852-861, 2006.
Definition of the Instantaneous Spatial Response
[0149] The present invention uses a priori knowledge of the imaging
system. Specifically the present invention either models or
measures the system's spatial response at an instant in time. The
spatial response used by the present invention is different than
that commonly accepted as the system's PSF. A point spread function
(PSF) is a measure of the imaging system's spatio-temporal
sensitivity and includes the effects of beamforming. It is measured
by translating a point target in front of the transducer and
beamforming the receive echoes for each spatial location of the
point target. The point target is to typically translated in
azimuth at a fixed range, which generates a space-time
(azimuth-time) PSF. The responses used by the present invention are
purely spatial PSFs. In order to produce a two-dimensional (2D)
space-space (azimuth-range) PSF, the point target needs to be
translated in azimuth and range. At each point target location the
received signals are beamformed, and a three-dimensional (3D)
dataset (azimuth-range-time) is generated thereby. The 2D
(azimuth-range) spatial PSF used in the present invention is the 2D
matrix at one time index in the 3D beamformed dataset. Since the
space-space PSF is conceptually different than the conventional PSF
(space-time), the spatial PSF used herein is referred to as the
Instantaneous Spatial Response (ISR). The ISR is the purely spatial
sensitivity response of the system at an instant in time. The ISR
can be measured experimentally, modeled numerically using computer
simulation, or predicted analytically.
Linear Algebra Formulation of the Spatial Point Spread Function
[0150] The sensitivity field for a transducer during pulse-echo
imaging can be expressed as the product of a propagation matrix, S,
and a set of aperture weightings, w. The propagation matrix uses
superposition to describe the contribution of each transducer
element at each field point at an instant in time. The propagation
matrix S in the formulation below is a function of the transmit
aperture weights used in the transmit beamformer, the excitation
pulse, and the individual element impulse responses of the transmit
and receive apertures. Dynamic receive focusing is also applied in
the formulation described herein, by adjusting the receive delays
12 of each individual element. Delays are updated with depth, and
update rates can vary. The delays are typically applied through a
combination of a FIFO (first in, first out) buffer which applies
whole sample delays and an FIR interpolation filter to apply
sub-sample delays. The FIR filters of the present invention may be
applied directly after the FIR interpolation filters or may be
designed so as it incorporate the interpolation process. Accurate
subsample interpolation would likely increase the length of the
filters described herein, but the overall hardware complexity may
be reduced by combining these features. The sensitivity field for a
transducer during pulse-echo imaging can be expressed as the
product of a propagation matrix, S, and a set of aperture
weightings, w. The propagation matrix uses superposition to
describe the contribution of each transducer element at each field
point at an instant in time. The propagation matrix S in the
formulation below is a function of the transmit aperture weights
used in the transmit beamformer, the excitation pulse, and the
individual element impulse responses of the transmit and receive
apertures. Dynamic receive focusing is also applied in the
formulation described herein, by adjusting the receive delays 12 of
each individual element. Delays are updated with depth, and update
rates can vary.
[0151] The two way pulse echo propagation matrix, S, for a fixed
transmit aperture and a n element dynamically focused receive
aperture at a total number of p points in three dimensional space
is defined by:
S = [ s 1 , 1 s 1 , 2 s 1 , n s 2 , 1 s p , 1 s p , n ] , ( 2 )
##EQU00001##
where s.sub.zk,i,j is the contribution of the jth element at the
ith point in space for the kth filter tap. Adequate spatial and
temporal sampling of the three dimensional yields very large
propagation matrices, and therefore, for simplicity, the present
disclosure describes analysis in two spatial dimensions only, i.e.,
azimuth and range, and assume a temporal sampling rate of 40 MHz
for the FIR filters 18. This is not meant to be limiting of the
invention as extension to three spatial dimensions and alternate
sampling rates is straightforward, although requiring more
computation time.
[0152] The receive FIR filter tap weights, W.sub.FIR, can also be
written in vector form as:
w=[w.sub.1 w.sub.2 w.sub.3 . . . w.sub.n].sup.T, (3)
where T denotes the vector transpose operation. Using (2) and (3),
the complete two-way pulse echo system PSF, .rho., can be defined
as:
P=Sw, (4)
i.e., the propagation matrix multiplied by the receive weighting
vector. Note that this results in the one dimensional column
vector, .rho., of length p the total number of points in three
dimensional space where the system PSF is measured.
[0153] To expand the formulation to include receive channel FIR
filters 18, it is noted that the final spatial PSF is a linear
superposition of multiple dynamically focused 2-way PSFs (wherein a
"2-way PSF" refers to a pulse-echo PSF or a transmit and receive
PSF). A new propagation matrix, S.sub.FIR is defined that is the
result of a simple combination of the propagation matrices
associated with each dynamic receive focus. The number of
propagation matrices included corresponds to number of FIR filter
taps, k:
S FIR = [ S z 1 , S z 2 , S z 3 , , S zk ] = [ s z 1 , 1 , 1 s z 1
, 1 , 2 s z 1 , 1 , n s z k , 1 , 1 s zk , 1 , 2 s z k , 1 , n s z
1 , 2 , 1 s z k , 2 , 1 s z 1 , p , 1 s z 1 , p , n s z k , p , 1 s
z k , p , n ] , ( 5 ) ##EQU00002##
where s.sub.zk,i,j is the contribution of the jth element at the
ith point in space for the kth filter tap. Adequate spatial and
temporal sampling of the three dimensional ISR yields very large
propagation matrices, and therefore, for simplicity, the present
disclosure describes analysis in two spatial dimensions only, i.e.,
azimuth and range, and assume a temporal sampling rate of 40 MHz
for the FIR filters 18. This is not meant to be limiting of the
invention as extension to three spatial dimensions and alternate
sampling rates is straightforward, although requiring more
computation time.
[0154] The receive FIR filter tap weights, w.sub.FIR, can also be
written in vector form as:
w.sub.FIR=[w.sub.z1.1 w.sub.z1.2 w.sub.z1.3 . . . w.sub.z1.n . . .
w.sub.zk.1 w.sub.zk.2 w.sub.zk.3 . . . w.sub.zk,n].sup.T. (6)
where w.sub.zk,j is the weight applied for the k.sup.th receive
focus on the j.sup.th receive element of the array 2. Using (5) and
(6), the complete two-way pulse echo system PSF for the receive
channel FIR beamformer 10 using k-taps 20T on each channel 16 is
written as follows:
P.sub.FIR=S.sub.FIRw.sub.FIR. (7)
Algorithm for Computing the FIR Filter Tap Weights
[0155] The cystic resolution metric described in Ranganathan et
al., "Cystic Resolution: A Performance metric for Ultrasound
Imaging Systems", IEEE Trans. On Ultrason., Ferroelec. And Freq.
Control, Vol. 54, No. 4, April, 2007, quantifies the contrast at
the center of an anechoic cost embedded in a speckle generating
background. Note that this metric measures contrast at a specific
point in space (the center of the cyst) at an instant in time. This
is a different parameter than the overall cystic contrast computed
from a B-mode image. Therefore the result computed when using the
cystic resolution metric is referred to as a "point contrast" to
avoid confusion with the overall cystic contrast. The point
contrast of the center of a cyst relative to the background,
neglecting electronic noise, can be defined as:
C = E out E tot ( 8 ) ##EQU00003##
where E.sub.out is the ISR energy outside the cyst and E.sub.tot is
the total ISR energy. The contrast resolution metric identifies the
contribution of specific points in the system's instantaneous
spatial response to the overall contrast. Note that if all of the
ISR energy lay within the cyst, C would be 0, indicating the best
possible contrast. On the other hand, if most of the ISR energy
lies outside the cyst, C approaches a value of 1. Therefore, when
contrast curves are plotted to show contrast as a function of cyst
radius, a relatively more negative dB value indicates relative
better contrast performance.
[0156] The FIR filter design algorithm uses the above cystic
resolution metric (point contrast of the center of the cyst C) to
formulate a least squares minimization problem with a quadratic
constraint. The weight values that result as the solutions to the
least squares minimization problem with a quadratic constraint are
referred to as quadratically constrained least squares (QCLS)
apodization profiles. Further details regarding the constrained
least squares techniques used can be found in Guenther et al.,
"Optimal Apodization Design for Medical Ultrasound Using
Constrained Least Squares Part I: Theory" IEEE Trans. On Ultrason.,
Ferroelec. And Freq. Control, Vol. 54, No. 2, February, 2007 and in
Guenther et al., "Optimal Apodization Design for Medical Ultrasound
Using Constrained Least Squares Part II: Simulation Results" IEEE
Trans. On Ultrason., Ferroelec. And Freq. Control. Vol. 54, No. 2,
February, 2007, both of which are hereby incorporated herein, in
their entireties, by reference thereto.
[0157] The algorithm for computing the FIR filter tap weights
utilizes the linear algebraic representation of the ISR presented
above. The contrast is optimized according to equation (8) by
minimizing the ratio of ISR energy outside a specified cyst
boundary to the total ISR energy. This is equivalent to minimizing
the ratio of ISR energy outside the cyst to ISR energy inside the
cyst, which can be expressed as:
min w S out w 2 subject to the quadratic constraint S in w 2 = 1 ,
( 9 ) ##EQU00004##
where .parallel. .parallel..sup.2 denotes the square of the
l.sup.2-norm, which is the square root of the dot product of a
vector with itself. For example, for x=[x1, x2, x3], the
l.sup.2-norm of x=sqrt(x1.sup.2+x2.sup.2+x3.sup.2). The
l.sup.2-norm is also called the Euclidean norm. S.sub.out is the
propagation matrix for all the spatial points of the ISR lying
outside the cyst boundary, and S.sub.in is the propagation matrix
for all the spatial points of the ISR lying inside the cyst
boundary. Note that the quadratic constraint minimizes the ratio of
ISR energy outside the cyst to ISR energy inside the cyst. The
optimal receive aperture weighting satisfying the quadratic
constraint is the eigenvector, w.sub.eig, corresponding to the
minimum eigenvalue resulting from the generalized eigenvalue
decomposition problem of S.sub.out.sup.TS.sub.out and
S.sub.in.sup.TS.sub.in; see Gander, "Least Squares With a Quadratic
Constraint". Numerische Mathematik, col. 36, pp. 291-307, 1981,
which is hereby incorporated herein, in its entirety, by reference
thereto. The generalized eigenvalue problem for a matrix pair (A,
B) both n by n matrices, is finding the eigenvalues, .lamda..sub.k,
and the eigenvectors, x.sub.k.noteq.0, such that:
Ax.sub.k=.lamda..sub.kBx.sub.k. (10)
[0158] The problem described in equation (10) above can be
efficiently computed and solved using MATLAB (The Mathworks, Inc.,
Natick, Mass.) with the eig( ) function. An important advantage of
the QCLS technique described herein, compared to other least
squares beamforming techniques, is that no matrix inversion is
required to solve for the optimal apodization profile.
[0159] Note that cyst size is an important parameter in the QCLS
apodization design method: specifying the propagation matrices in
equation (9) and implicitly defining mainlobe size in the resulting
ISR. ISRs constructed with QCLS profiles designed for larger cysts
will naturally have a large mainlobe, but lower overall sidelobe
levels i.e., lower overall heights of the sidelobes. The term
"design cyst size" is used as a convenient way to differentiate
between apodization (QCLS) profiles that contain different sets of
tap weights. Every design cyst size will produce a different,
optimal QCLS profile, yet experience shorts that the general shape
of the QCLS at eights remains similar over a range of cyst sizes.
Furthermore, a set of apodization profiles can be produced to
achieve optimal contrast for any particular cyst size. A "QCLS
profile" is an apodization profile computed via the QCLS algorithm.
The FIR filter weights can be considered as a series of sequential
QCLS profiles. This analogy is imperfect however as the FIR filter
weights consider the combined effect of each of the weights, while
simple stringing together QCLS apodization curves would not
generate the same useful synergy.
Designing the FIR Filter Weights with Varying Spatial
Sensitivity
[0160] The FIR Filter weights designed using the algorithm above
are determined to optimize the point cystic contrast. While this
metric is particularly valuable for assessing system performance,
there are some situations where the challenges of imaging in the
body are not fully encompassed within this metric. For example
during ultrasound imaging of the internal organs (e.g. liver) the
imaging system must contend with extremely bright echoes
originating from gas within the bowel. Although the bowel may be at
some distance, and thus the ISR in that region may have a low
value, the extreme echogenicity of bowel gas may significantly
degrade the local image contrast within the liver. In this
situation, and many others, it is thus desirable to more strongly
suppress the ISR energy at greater distances from the cyst (focal
point). In other instances, it may be desirable to increase the
importance/levels of sidelobes to become increasingly greater as
the distance outside the cyst boundary grows.
[0161] To design FIR apodization weights with varying spatial
sensitivity one need only apply the design equation described above
in equation (9) using a modified version of the ISR. In the most
general situation the spatial sensitivity both within and outside
the cyst can be modified so that:
min w p S out w 2 subject to the quadratic constraint q S in w 2 =
1 , ( 9 a ) ##EQU00005##
[0162] Where .rho. is a vector with a value for each location
outside the cyst weighted by the inverse of its desired
significance in the final solution. Thus a location that is to be
strongly minimized in the final solution should have a high value
in .rho.. Likewise, q is a vector with a value for each location
inside the cyst weighted by its desired significance in the final
solution. Thus a point that should be maximized should have a high
value in q. Although this expression may seem to complicate the
solution of the FIR filter weights, simple grouping of the terms
yields the following minimization problem:
min w T out w 2 subject to the quadratic constraint T in w 2 = 1 ,
( 9 b ) ##EQU00006##
[0163] Where T.sub.out=.rho.S.sub.out and T.sub.in=qS.sub.in. It is
of course straightforward to solve this problem using the
generalized eigenvalue decomposition approach described above. It
is also straightforward to populate either .rho. or q with ones to
make the relative weighting outside or inside the cyst uniform. The
robust algorithm for computing FIR filter Weights can also be
adjusted using this method.
Robust Algorithm for Computing the FIR Filter Tap Weights
[0164] The QCLS design algorithm disclosed above offers substantial
improvements over conventional apodization methods and is
straightforward to implement. The above method is limited however
in that it does not explicitly consider the impact of noise on
image contrast and can thus design FIR filter weights that are
ineffectual in noisy environments. An alternate design approach,
described below can be employed to explicitly consider noise and
thereby generate FIR beamformer weights that are robust to noise.
While design using this "robust" method is somewhat more complex,
that complexity is likely well worth the achieved improvement in
performance.
Generalized Cystic Resolution Metric
[0165] One important effect of a receive beamformer is to improve
the signal to noise ratio of the received waveforms/signals. The
beamforming architecture of the present invention is constructed to
maximize the contrast resolution of the system. If the FIR filter
weights are designed considering pure cystic contrast, with no
consideration of electronic noise, then the resultant beamformer
will offer improved contrast resolution in high SNR environments,
but may not offer adequate SNR in other environments. If the SNR of
signals input to the beamformer is taken into account in the FIR
filter weight design it is possible to balance sensitivity (SNR
gain) and contrast resolution. With this and other possible design
assumptions it is important to analyze how the receive channel FIR
filters affect the system's sensitivity. Liu et al., in "Correction
of ultrasonic waveform distortion using backpropagation and a
reference waveform method for time-shift compensation", J. Acoust.
Soc. Amer., vol. 96, no. 2, pp. 649-660, 1994, defined a rigorous
measure of a beamformer's echo signal-to-noise ratio (SNR) to
compare the sensitivities of various beamforming strategies such as
the conventional delay-and-sum (DAS) beamformer and the spatial
matched filter (SMF) beamformer. The disclosed analysis in Liu et
al. however ignored contrast resolution performance.
[0166] A generalized cystic resolution (GCR) metric, as described
in Ranganathan et al. (cited above) can be used to simultaneously
characterize the contrast resolution and SNR performance of an
arbitrary beamformer. The GCR metric is thus used to analyze the
performance of the FIR beamformer 10 according to the present
invention, compared to a conventional DAS beamformer 1000. Results
are presented as simple curves, which plot cystic resolution either
as a function of cyst size or input channel SNR. Performance
improvements are easily depicted and determined by the beamformer
that achieves better cystic resolution at a smaller cyst size or
worse input SNR. When analyzed with the generalized cystic
resolution metric, by plotting cystic contrast versus cyst size,
the set of QCLS apodization profiles will generate a lower bound on
cystic contrast for the FIR beamformer 10 and DAS beamformer 1000,
given the specified system characteristics. Since scanning through
all the different apodization profiles would not be realistic in a
real-time clinical setting, it is interesting to see how the
apodization profile (or FIR filter weights) designed for a specific
cyst size performs over a range of cyst sizes.
[0167] A further description of the generalized cystic resolution
metric follows. For an even more thorough explanation, see
Guenther, D. A. and W. F. Walker, "Generalized Cystic Resolution: A
Metric for Assessing the Fundamental Limits on Beamformer
Performance," IEEE Transactions on Ultrasonics, Ferroelectrics, and
Frequency Control, vol. 56, no. 1, pp. 77-90, 2009, which was
incorporated by reference above. For an n element linear array
(where "n" is a positive integer) consisting of equally spaced
sensors operating in pulse-echo mode, the time record of the
receive signal at the output of the beamformer is:
y ( t ) = .intg. - .infin. + .infin. k = 1 N w k P k ( x _ , t ) N
( x _ ) x _ + k = 1 N w k E k ( t ) . ( 11 ) ##EQU00007##
[0168] Note that the integration performed over three-dimensional
space. P.sub.k({right arrow over (x)},t) is the spatio-temporal
response of the k.sup.th receive element, where w.sub.k is the
weight applied to the k.sup.th receive element. N({right arrow over
(x)}) is the target scattering function assumed constant with time;
and E.sub.k(t) is the electronic noise on the k.sup.th receive
channel. The spatial and temporal dependence of the weights has
been omitted for clarity. All transmit conditions are incorporated
into P.sub.k({right arrow over (x)},t) including transmit
apodization, transmit aperture spatial impulse response,
electromechanical impulse response, etc.
[0169] A beamformer's performance is typically analyzed at an
instant in time. In order to avoid confusion between the purely
spatial response of an element and the full four-dimensional PSF of
an element, the purely spatial response is referred to herein as
the Instantaneous Spatial Response (ISR), P.sub.k({right arrow over
(x)},t.sub.o) as noted above, where t.sub.o denotes an instant in
time. The ISR measures the sensitivity of the system, including all
aspects of beamforming, at all spatial locations at an instant in
time. The PSF would be the time record of all the system ISRs.
Using a linear algebra formulation for a receive element's ISR, it
has been shown that the signal-to-noise ratio (SNR) and cystic
resolution (CR) at the output of the beamformer can be expressed as
[1]:
SNR out = .DELTA. x _ 2 .sigma. N 2 w T R tot w w T R E w , ( 12 )
CR = .DELTA. x _ 2 .sigma. N 2 w T ( R out + R E ) w .DELTA. x _ 2
.sigma. N 2 w T ( R tot + R E ) w , ( 13 ) ##EQU00008##
[0170] Note that these values are calculated at an instant in time.
The R.sub.tot matrix represents the inner product of the
propagation matrix describing the ISR of the aperture at all points
in space. The propagation matrix has columns corresponding to the
spatially sampled individual receive element ISRs. The R.sub.out
matrix represents the inner product of the propagation matrix
describing the ISR at all spatial points that lie outside a
specified cyst boundary. The constant .sigma..sup.2.sub.N is the
variance of the target scattering function, which is modeled as a
stationary zero-mean, multivariate normal (MVN) stochastic process:
N({right arrow over (x)}).about.MVN(0,.sigma..sub.N.sup.2,I), where
I is an identity matrix. R.sub.E is the noise autocovariance
matrix. The .DELTA..sub.{right arrow over (x)} term is a constant
related to the volume of the discrete spatial sampling and accounts
for the approximation of the continuous spatial integral in
equation (11) with the linear algebra formulation using a discrete
summation of vectors. It is assumes that the noise is spatially and
temporally uncorrelated so its autocovariance matrix reduces to:
R.sub.E=.sigma..sup.2.sub.EI. Without loss of generality, one can
combine the .DELTA..sub.{right arrow over (x)} constant, the
scattering medium's variance, .sigma..sup.2.sub.N, and noise
variance, .sigma..sup.2.sub.E, into one parameter,
.sigma..sub.load.sup.2=.sigma..sub.E.sup.2/.DELTA..sub.E.sup.2.sigma..sub-
.N.sup.2, and simplify the above equations:
SNR out = w T R tot w .sigma. load 2 w T w , ( 14 ) CR = w T ( R
out + .sigma. load 2 I ) w w T ( R tot + .sigma. load 2 I ) w , (
15 ) ##EQU00009##
[0171] Note that the .sigma..sup.2.sub.load parameter is a scaled
version of the noise variance, and in most clinical imaging
scenarios quantifying .sigma..sup.2.sub.N is intractable. Typically
cystic resolution curves are presented as a function of receive
channel input SNR and cyst radius. Input SNR into the beamformer on
one channel is calculated as:
SNR in = .DELTA. x _ 2 .sigma. N 2 w k S k T S k w k w k R E k w k
= S k T S k .sigma. load 2 . ( 16 ) ##EQU00010##
[0172] S.sub.k is a vector describing the ISR for one receive
channel, k, and R.sub.E.sub.k is the noise autocovariance on the
kth channel. Like SNR.sub.out and CR above, input SNR, SNR.sub.in,
is also calculated at an instant in time. Given the system's
spatial response and assumptions about the noise statistics, input
SNR to the beamformer is simply a function
.sigma..sup.2.sub.load.
Implementation
[0173] By describing the ISRs for every point in the final image, a
full set of optimal dynamic receive aperture weights (i.e., tap
weights) for the beamformer 10 can be calculated. In the most
generic implementation, the calculated receive aperture weights
require the FIR filters 18 to be spatially and temporally variant
relative to one another. Consequently in order to achieve this
spatial and temporal variance, this would require computing a new
set of channel unique FIR filters for each image point. A simpler
embodiment of the present invention employs a linear array 2 with
no beamsteering, so that the FIR filters 18 on each channel are
only depth dependent. While the most generic implementation would
require independent filter weights at each range, empirical
experimentation has shown that these weights need not vary rapidly
over range to achieve excellent image contrast. Alternate
implementations might employ beamsteering for more generic imaging
and would in turn require varying the filter taps across scan
angle.
[0174] Once the set of receive channel FIR filters has been
computed, the implementation of the FIR beamformer 10 is
straightforward. In order to clarify implementation, reference is
made back to the five-tap FIR beamformer architecture in FIG. 2. At
an instant in time, t.sub.i, each tap 20T on each receive channel
has one RF sample. Taps B, G (not shown) and L have the RF samples
associated with one particular receive focus, z.sub.i. Taps A, F
(not shown) and K have RF samples associated with receive focus
z.sub.i+1, taps C, H (not shown) and M have RF samples associated
with receive focus z.sub.i-1, taps D, I (not shown) and N have RF
samples associated with receive focus z.sub.i-2, and taps E, J (not
shown) and O have RF samples associated with receive focus
z.sub.i-3. At this instant in time all RF samples on every channel
are multiplied by their respective tap weights and summed in order
to form one FIR beamformed sample in the output RF line. Note that
the embodiment of FIG. 2 assumes a symmetrical array and therefore
a system without beamsteering. This is just one possible embodiment
and alternative implementations without such limitation are
straightforward.
[0175] At the next instant in time, t.sub.i+1, an entire new set of
five-tap FIR filter weights for each channel are loaded (the FIR
filters are depth dependent). (As stated above, the same FIR filter
weights may be reused to simplify implementation, often with little
reduction in image quality.) The RF samples with receive focus
z.sub.i+1 that were associated with taps A, F (not shown) and K
move to taps B, G (not shown) and L, respectively. Likewise the RF
samples with receive focus z.sub.i associated with taps B, G (not
shown) and L move to taps C, H (not shown) and M, respectively, the
RF samples with receive focus z.sub.i-1, associated with taps C, H
(not shown) and M move to taps D, I (not shown) and N,
respectively, and the RF samples with receive focus z.sub.i-2
associated with taps D, I (not shown) and N move to taps E, J (not
shown) and O, respectively. The RF samples that were in E, J (not
shown) and O are discarded. A new set of RF samples with receive
focus z.sub.i-2 move into the FIR beamformer at taps A, F (not
shown) and K. Then all RF samples are multiplied by their
respective tap weights and summed, forming the next sample in the
FIR beamformed A-line. This process repeats until the entire summed
RF line has been formed. The determination as to when an entire
summed RF line is complete is typically, dependent upon a user
setting which is based on the depth to which the user wishes to
penetrate/image an object. Most imaging systems have a knob for
user operation to set the scan depth. Scan converter 45 forms a
B-mode image from a number of A-lines based on a function of frame
rate, depth, channel number, display screen, and transducer size. A
typical number of A-lines used to form a B-mode image ranges from
about 256 to about 1024, although this may vary. Typically, the
user selects a tradeoff between framerate and resolution. At a high
framerate and low resolution the beams will be broad and there will
be fewer A-lines per image. At low frame-rate and high resolution
each beam is narrow and more beams are needed to form a single
image. In addition, some systems allow the user to select the width
of the scan, which also alters the number of A-lines. Thus, the
number of A-lines used to make up a B-mode image is largely
determined by the user interacting through the controller. The scan
converter 45 processes the A-Line data to form a B-Mode image.
[0176] FIG. 4 illustrates events that may be performed in a method
of applying FIR filter based dynamic receive apodization to a
broadband imaging signal according to an embodiment of the present
invention to optimize contrast and resolution of an image produced
therefrom. At event 410, a user may optionally select parameters
defining FIR an apodization, including selection of a set of tap
weights to be used initially in the FIR filters 18. Alternatively,
if the user does not make a selection, the system 100 may, use a
default FIR scheme, including a default set of initial tap
weights.
[0177] At event 412, the system 100 receives multiple channels of
broadband signals generated from waves reflected off of an object
to be imaged. Array 2 may be used to transduce the received signals
to RF signals that are input to receive beamformer 10. The
broadband signals may be signals generated by reflecting energy off
of any type of object that will reflect the energy, using any type
of broadband imaging system. In at least one embodiment, the
broadband imaging system is an ultrasound imaging system. In at
least one embodiment, the object is living tissue or is located in
living tissue. In at least one embodiment, the energy is reflected
off of the object during an in vivo procedure.
[0178] After applying the appropriate delays 12 the channels of
signals are then weighted at event 414 using dynamic FIR filters 18
with the currently selected tap weights. Next, at event 416 the
weighted outputs from the taps are summed across time and channel
number to yield an RF sample used to form an A-line. At event 420,
it is determined at the envelope detector 40 whether there are a
sufficient number of samples to form an entire A-line. If there are
not yet a sufficient number, then a new FIR apodization profile is
automatically selected at event 422 to replace the existing FIR
filter weights. These weights differ from those being replaced as a
function of the change in distance (represented by the change in
sample time).
[0179] Processing then returns to event 412, where the signals
advance in a manner as described above, and then at event 414 the
channel signals are multiplied by the dynamic FIR filters using the
new current weights (i.e., new tap weights). Events 422, 414, 416
and 420 are iterated until such a entire A-line can be formed. As
noted above, the QCLS profiles change as a function of distance
from the array to the object. When a sufficient number of samples
have been formed to make an A-line at event 420, then the A-line is
outputted at event 424 by envelope detector 40 to scan converter
45. At event 426 it is determined whether a sufficient number of
A-lines have been received by the scan converter 45 from envelope
detector 40 to generate a B-mode image. The scan converter 45
accumulates the A-line to form a B-mode image, which is then
outputted to purge the scan converter 45 of the current A-lines,
and the B-mode image is displayed on display 50 at event 428. An
exemplary three-dimensional scan converter is described in U.S.
Pat. No. 5,546,807.
[0180] FIG. 5 is a schematic illustration of a user interface 500
including display 50 upon which images generated by processing
according to the present invention are displayable. Additionally,
user interface may include a user selectable feature that allows a
user to select a particular set of tap weights to be used in the
FIR filters 18, such as at event 410 for example. These tap weight
are selected based on cyst size. Additionally, the user may also
select a desired SNR/beamformer sensitivity. A further alternative
is to provide the system with a user adjustable feature such as a
knob, wherein the user can adjust the knob to select an acceptable
tradeoff between image resolution and image contrast, which is
accomplished by varying the tap weights/cyst size in the same
manner described above, but only the interface to the user is
provided differently. As an example of cyst size selection, by
mouse-clicking or using some other input gesture to select button
512, a menu 514 may pop up on display 50. From this menu, the user
can select a cyst size that will determine the tap weights to be
used in the FIR filters 18. The tap weights are stored in one or
more look-up tables 600.
[0181] FIG. 6 illustrates the tap weights having been
pre-calculated for a cyst radius of about 0.3 mm at various
distances I through Y, for each channel number (while there are a
total of five channels for the example shown in FIG. 2, the
assumption of symmetry allows storage of only three channels worth
of taps). Because of the assumption of symmetry, only (X-1)/2+1
(for an odd number of channels) or X/2 (for an even number of
channels) columns of weights need be stored (a total of three
columns for the example of FIG. 2. For each distance, a tap weight
20 is stored for each tap of each FIR filter (channel). At event
422, the system increments from the current distance, to the next
consecutive distance, selects the tap weights in the row for that
distance and replaces the current tap weights with the newly
selected tap weights.
Robust FIR Beamformer
[0182] The QCLS apodization design algorithm described above can be
used in a FIR beamformer 10 that produces optimized cystic
resolution superior to the DAS beamformer 1000, by applying
multi-tap 20 FIR filters 18 in the beamformer 10 as described above
(e.g., see FIG. 2) while ignoring electronic noise. In the
previously described embodiments, the QCLS algorithm minimized
equation (15) in the absence of noise (.sigma..sup.2.sub.load=0).
In the robust FIR beamformer embodiments, the QCLS algorithm is
extended to include system SNR by setting a particular
.sigma..sup.2.sub.load value. In the following examples we assume
an overly simplistic model For electronic noise. Specifically we
assume that the electronic noise is modeled as a multivariate
normal stochastic process which is uncorrelated in time and across
receive channel. This simplifies the noise autocovariance matrix,
R.sub.E=.sigma..sup.2.sub.EI, where I is an identity matrix. In
certain scenarios designers may wish to use a more general noise
model, or estimate the noise autocovariance experimentally or
analytically. Mathematically incorporating noise into the QCLS
design procedure constrains the beamformer's output SNR. In this
scenario the robust QCLS algorithm minimizes the CR equation in
(15), which includes the .sigma..sup.2.sub.load diagonal loading
term. The optimal QCLS apodization profile that minimizes CR is the
eigenvector associated with the minimum positive eigenvalue from
the generalized eigenvalue decomposition problem of matrices
(Rout+.sigma..sup.2.sub.loadI) and (Rtot+.sigma..sup.2.sub.loadI).
Note that a new optimal robust QCLS apodization profile is
calculated for each value of .sigma..sup.2.sub.load. The
generalized eigenvalue problem for a matrix pair (A, B) both n by n
matrices, is finding the eigenvalues, .lamda..sub.k, and the
eigenvectors x.sub.k.noteq.0, such that:
Ax.sub.k=.lamda..sub.kBx.sub.k. (17)
[0183] This eigenvalue problem is efficiently computed using the
eig() function in MATLAB. Although implementation of the QCLS
algorithm with diagonal loading is conceptually simple, the effect
that this modification has on the resultant optimal weights and
beamformer response is unclear. In general, increasing
.sigma..sup.2.sub.load during the QCLS apodization design procedure
will maiden the response's mainlobe, raise sidelobe levels, and
improve SNR performance of the receive beamformer. In order to
further highlight the relationship between SNR and CR of the
beamformer, three different cases for the loading constant are
described as follows:
CASE I: .sigma..sup.2.sub.load=0, infinite electronic SNR
[0184] Given this loading value, equation (15) becomes equation
(18) as follows:
CR = w T R out w w T R tot w , ( 18 ) ##EQU00011##
[0185] Equation (18) is the equation for cystic resolution in the
absence of noise. According to equation (14), the output SNR of the
beamformer is infinite since .sigma..sup.2.sub.load=0.
[0186] Equation (18) is the cost function minimized to produce the
quadratically constrained least squares (QCLS) apodization profiles
for optimal cystic contrast in the examples described above,
previous to the description of the robust FIR beamformer. The
results (see Example 1 below) showed that a 20 dB improvement in
cystic resolution, relative to the DAS beamformer of FIG. 1, was
achievable with the QCLS algorithm and the receive FIR beamformer
architecture of FIG. 2. However, this increase in contrast
resolution came with a significant loss in beamformer
sensitivity.
CASE II: maxeigenvalue(Rout)<<.sigma..sup.2.sub.load, poor
electronic SNR
[0187] The function eigenvalue(A) denotes a column vector
containing all the eigenvalues of matrix A. Note that both
R.sub.out and R.sub.tot are n by n full rank matrices and therefore
will have n distinct eigenvalues. The maximum eigenvalue of
R.sub.out will be less than the maximum eigenvalue of R.sub.tot
because R.sub.out represents only a fractional portion of the total
ISR energy specified by the matrix R.sub.tot. For this
.sigma..sup.2.sub.load case, the R.sub.out matrix in the numerator
of the CR equation is dominated by the diagonal loading:
CR = w T ( R out + .sigma. load 2 I ) w w T ( R tot + .sigma. load
2 I ) w .fwdarw. w T ( .sigma. load 2 I ) w w T ( R tot + .sigma.
load 2 I ) w = .sigma. load 2 w T w .sigma. load 2 w T w + w T R
tot w . ( 19 ) ##EQU00012##
[0188] Applying the QCLS optimal apodization design algorithm, the
minimization of equation (19) in order to produce optimal contrast
is the same as maximizing the inverse of equation (19):
max w 1 CR = max w .sigma. load 2 w T w + w T R tot w .sigma. load
2 w T w = max w ( 1 + w T R tot w .sigma. load 2 w T w = max w SNR
out . ( 20 ) ##EQU00013##
[0189] For this case of diagonal loading (poor electronic SNR), the
apodization profile that produces optimal contrast is the
apodization profile that maximizes the SNR at the output of the
receive beamformer. This makes intuitive sense; in a noisy
environment, the beamformer maximizes the SNR in order to optimize
contrast.
Case III: maxeigenvalue(Rout)<<.sigma..sup.2.sub.load,
extremely poor electronic SNR
[0190] In the extreme case that the noise power far exceeds the
sensitivity of the system, i.e. SNR=0, the cystic resolution
equation becomes:
CR = w T ( R out + .sigma. load 2 I ) w w T ( R tot + .sigma. load
2 I ) w .fwdarw. w T ( .sigma. load 2 I ) w w T ( .sigma. load 2 I
) w = .sigma. load 2 w T w .sigma. load 2 w T w = 1. ( 21 )
##EQU00014##
[0191] The R.sub.out and R.sub.tot matrices are dominated by the
loading term. In this case it does not matter what the beamformer
weights are, the noise completely dominates any relevant signal
making the cyst undetectable.
[0192] The three .sigma..sup.2.sub.load cases point to an
interesting relationship between beamformer output SNR and CR.
Depending on the level of diagonal loading, or input SNR into the
beamformer, the optimal QCLS beamformer weights change from
minimizing CR (when .sigma..sup.2.sub.load=0), to maximizing SNR
(when maxeigenvalue(R.sub.tot)<<.sigma..sup.2.sub.load), to
being completely arbitrary (when
maxeigenvalue(R.sub.tot)<<.sigma..sup.2.sub.load). In other
words, .sigma..sup.2.sub.load parameterizes the QCLS beamformer's
cystic resolution as a function of SNR. Therefore, receive channel
input SNR can be viewed as a design parameter, and optimal
operating conditions can be determined along the SNR-CR design
curve. Note that in all loading cases the QCLS algorithm minimizes
the cystic resolution equation in (15).
Example SNR-CR Design Curves
[0193] The .sigma..sup.2.sub.load parameter can be used with the
GCR metric to investigate the robustness of an arbitrary beamformer
under different input SNR conditions. In the present invention,
.sigma..sup.2.sub.load is used as a design parameter in the QCLS
algorithm when constructing the FIR filters 18 for the robust FIR
beamformer. In order to differentiate between when the
.sigma..sup.2.sub.load parameter is used in the QCLS design
algorithm and when it is used for analyzing SNR performance in the
generalized cystic resolution metric, it is referred to herein as
.sigma..sup.2.sub.design when used as a design parameter and
.sigma..sup.2.sub.load when used in the metric.
[0194] FIG. 7A plots an exemplary SNR-CR design curve 650 for an
arbitrary beamformer. Each point along the design curve represents
a different .sigma..sup.2.sub.design value and a different, optimal
apodization window. For each window, cystic resolution was computed
by substituting .sigma..sup.2.sub.design for .sigma..sup.2.sub.load
in equation (15). In terms of the GCR metric, plot 650 corresponds
to a plane at a constant cyst radius. As the value of the design
loading parameter, .sigma..sup.2.sub.design, increases, the
operating point moves to the left along the curve 650 and the
design SNR decreases. Note that the "optimal window" would lie at
the bottom left hand corner of FIG. 7A (increased contrast at poor
SNR). On the right end of the design curve 650 is the maximum
contrast resolution window 652 (i.e., Case I, described above).
Near the other end of the SNR-CR design curve 650 lies a window 654
that maximizes beamformer sensitivity (i.e., Case II, described
above). Further increasing .sigma..sup.2.sub.design from this point
(i.e., moving further left along the curve 650) does not change the
optimal profile until computation reaches machine precision and the
weights become completely arbitrary at window 656 (i.e.. Case III
described above). Using the shape of the design SNR-CR curve 650,
one can easily quantify and visualize the tradeoff between
sensitivity and contrast. The present invention identifies the
"optimal" window 658 at the bottom "knee" of the sigmoidal SNR-CR
design curve 650. At this point the beamformer 10 is achieving
similar cystic resolution compared to the optimal contrast window
652 as well as increasing SNR performance.
[0195] FIGS. 7B-7E shows QCLS apodization profiles 660, 662, 664,
666 from different points along the SNR-CR design curve 650
according to points 656, 654, 658 and 652, respectively. FIGS.
7F-7I show cystic resolution curves 668, 670, 672, 674 for the four
different windows 656, 654, 658 and 652, respectively, when
analyzed using the GCR metric. These cures quantify performance of
the different windows as a function of receive channel SNR (varying
.sigma..sup.2.sub.load) at a constant cyst radius. Note that these
curves would intersect the SNR-CR design curve at the Case III 656,
optimal SNR 654, "knee" 658, and optimal CR 652 operating points on
curve 650, respectively.
[0196] In general, as the design loading parameter increases, the
beamformer's sensitivity increases while the contrast resolution
performance decreases. However, given the sigmoidal shape of curve
650, for a slight decrease in contrast, large gains in sensitivity
can be made, with these gains being maximized around the lower
"knee" 658 of the curve 650.
[0197] Using the QCLS algorithm with added SNR constraint makes it
possible to quantify the fundamental CR performance limits for any
imaging system that can be reasonable well characterized. This
lower bound would be a GCR surface; parameterized at every point by
a new set of apodization weights calculated using a particular
design SNR and design cyst radius. A user can select an operating
point (i.e., one set of tap weights 20T) on this lower bound
surface and then quantify that beamformer's clinical imaging
performance as a function of cyst size and input channel SNR using
the metric.
[0198] FIGS. 7A-7I highlight how the GCR metric can be used to
design beamformers. The graphical representation of the metric
condenses a great amount of information into simple curves (or
surfaces) so that clinical imaging performance of different
beamforming strategies can be evaluated. In the following sections
the metric is used to design a robust FIR beamformer and to compare
and analyze the diagnostic capabilities of several beamformer
architectures.
Arbitrary Weighting Functions for Improved Spatial Responses
[0199] In certain imaging scenarios the characteristics of the
system's point spread function (PSF) at specific spatial locations
may be more important than at other spatial locations. For example,
faster sidelobe rolloff may be desired when imaging near bone or
the trachea since these bright off axis targets will add clutter to
the image. In such situations, a spatial weighting function,
g({right arrow over (x)}), can be added to the QCLS algorithm that
emphasizes or deemphasizes certain locations in the system's
instantaneous spatial response.
[0200] For example, a weighting function g({right arrow over (x)})
can be applied to decrease sidelobe levels preferentially in
certain regions of the PSF. Such a weighting function can be
defined as:
g({right arrow over (x)})=|{right arrow over (x)}-{right arrow over
(x)}.sub.focus|.sup.o, (22)
where {right arrow over (x)}.sub.focus is the receive focus of the
aperture in three dimensional space and n=0, 1, 2, 3 . . . .
[0201] When n=0, no weighting is applied and as n increases, the
QCLS algorithm will tend to decrease sidelobes further away from
the focus at the expense of widening the mainlobe. A thorough
derivation for applying the weighting function to the QCLS
algorithm is described in Golub et al., Matrix Computations, 3 ed.
Baltimore: Johns Hopkins University Press, 1996, Which is hereby
incorporated herein, in its entirety, by reference thereto. The
weighted quadratically constrained least squares apodization
profiles resulting form application of the weighting function
described above are referred to as WQCLS (weighted quadratically
constrained least squares) apodization profiles, that include WQCLS
weights. FIR filters that use WQCLS apodization profiles are
referred to as FIR-WQCLS filters. The SNR design constraint and the
spatial weighting function can be combined to produce robust WQCLS
apodization profiles as well.
[0202] FIG. 8 illustrates a typical computer system, all or a
portion of which may be incorporated into a system according to an
embodiment of the present invention. The computer system 700
includes any number of processors 702 (also referred to as central
processing units, or CPUs) that are coupled to storage devices
including primary storage 706 (typically a random access memory, or
RAM), primary storage 704 (typically a read only memory, or ROM).
As is well known in the art, primary storage 704 acts to transfer
data and instructions uni-directionally to the CPU and primary
storage 706 is used topically to transfer data and instructions in
a bi-directional manner. Both of these primary storage devices may
include any suitable computer-readable storage media such as those
described above. A mass storage device 708 is also coupled
bi-directionally to CPU 702 and provides additional data storage
capacity and may include any of the computer-readable media
described above. It is noted here that the terms "computer readable
media" "computer readable storage medium" "computer readable
medium" and "computer readable storage media", as used herein, do
not include carrier waves or other forms of energy, per se. Mass
storage device 708 may be used to store programs, data and the like
and is typically a secondary storage medium such as a hard disk
that is slower than primary storage. It will be appreciated that
the information retained within the mass storage device 708, may,
in appropriate cases, be incorporated in standard fashion as part
of primary storage 706 as virtual memory. A specific mass storage
device such as a CD-ROM or DVD-ROM 714 may also pass data
uni-directionally to the CPU.
[0203] CPU 702 is also coupled to an interface 710, which may
include user interface 500, for example, and which may include one
or more input/output devices such as video monitors, track balls,
mice, keyboards, microphones, touch-sensitive displays, transducer
card readers, magnetic or paper tape readers, tablets, styluses,
voice or handwriting recognizers, or other well-known input devices
such as, of course, other computers. CPU 702 optionally may be
coupled to a computer or telecommunications network using a network
connection as shown generally at 712. With such a network
connection, it is contemplated that the CPU might receive
information from the network, or might output information to the
network in the course of performing the above-described method
steps. The above-described devices and materials will be familiar
to those of skill in the computer hardware and software arts.
[0204] The hardware elements described above may implement the
instructions of multiple software modules for performing the
operations of this invention. For example, instructions for
applying FIR apodization weights, instructions for summing,
instructions for looking up tap weights in the look-up tables,
instructions for envelope detection and instructions for displaying
a B-mode image, and/or other instructions and/or algorithms, such
as an algorithm for calculating tap weights, instructions fro
applying an arbitrary weighting function to the tap filters of the
FIR beamformer, etc. may be stored on mass storage device 708 or
714 and executed on CPU 708 in conjunction with primary memory
706.
Implementation with Complex Data
[0205] The majority of broadband ultrasound beamformers use
directly sampled RF data as described in the preceding embodiment.
In other domains, and in some ultrasound imaging systems however
the received data undergoes complex demodulation to reduce the
bandwidth required to carry signals throughout the system. Such
complex demodulation schemes are particularly common in broadband
communications, RADAR, and SONAR systems. One conventional
embodiment of such a system 1000C is shown in FIG. 9. The
transducer array 2 outputs signals to the demodulator circuits
4010. Demodulators 4010 each use an input demodulation waveform
(not shown) to determine both the demodulation frequency and phase.
In one simple embodiment each channel in the array uses an
identical demodulation waveform so that all signals are demodulated
at the same frequency and with the same phase. The demodulated
output 4015 comprises two signals that are considered to be
90.degree. out of phase from one another. These signals are
typically referred to as the In-Phase and Quadrature components, or
the I and Q components. Each channel has its own I and Q signal
representing the signal from the transducer array 2. The complex
demodulated signals 4015 are input to a focusing component 4020.
This focusing component may include a combination of FIFO memories
to implement whole sample time delays and a phase rotator to
implement sub-sample delays. Such a beamformer is described in
detail in U.S. Pat. No. 5,797,847 which is hereby incorporated by
reference in its entirety. The outputs of focusing components 4020
comprise focused I and Q signals 4025. These focused I and Q
signals are in turn summed by summers 24' to yield summed I and Q
signals 4035. These signals can then be envelope detected to form
an A-line or otherwise processed to estimate blood or tissue
velocities, or processed in any of a number of other manners to
extract useful information.
[0206] The complex beamformer 1000C of FIG. 9 can readily be
modified to incorporate the present invention as shown in FIG. 10.
The notable difference between the conventional beamformer 1000C of
FIG. 9 and the complex beamformer 10C according to the present
invention shown in FIG. 10 is the addition of the FIR filter banks
18'. The focused outputs 4025 from the focusing components 4020 are
input directly into the FIR filter banks 18'. These FIR Filter
banks incorporate banks of delays and weights analogous to those
shown in FIG. 2. The delayed and FIR filtered outputs 4029' of the
FIR filter banks 18' are then input to the summers 24' to form the
summed I and Q channels 4035'.
[0207] Unlike the FIR banks 18 of FIG. 2, the filter banks 18' may
incorporate separate I and Q channel FIR filters. In one embodiment
the filter banks 18' incorporate weights as simple phase rotations
with amplitude scaling. Such an approach is necessary to maintain
orthogonality (90.degree. phase difference) between the I and Q
channels. Mathematically such weights for a single tap of the
complex FIR filter 18' can be applied using equation (23):
I''+jQ''=(A+jB)(I'+jQ')=(AI'-BQ')+j(AQ'+BI') (23)
[0208] This weighting scheme can be readily implemented using the
present invention. The FIR weight design methods described above
can also be applied in a straightforward manner to determine
optimal weights by simply using complex ISRs and complex
weights.
Using FIR Apodization to Expand the Depth of Field on Transmit
[0209] While high-end ultrasound imaging systems universally use
dynamic receive focusing to apply optimal focusing throughout range
on receive, their transmit focusing capability is much more
limited. If a low f-number is used on transmit then fine image
resolution is possible at the focus, but the short depth of field
will result in poor transmit resolution away from the focus. If a
higher f-number is used on transmit then the resolution at the
focus will be degraded, but this resolution will degrade more
slowly away from the focus. Apodization of the transmit aperture
offers some ability to balance focal resolution and depth of field.
This problem has previously been addressed by both Hossack and
Ranganathan (see references above), although both of the proposed
methods have limitations that limit their utility. Hossack's method
requires transmit waveforms consisting of long temporal sequences
and subtle waveform changes which may be difficult to implement in
modern hardware. Ranganathan's approach requires a desired system
response as an input. As the characteristics of an ideal response
is well known, but its actual shape is not, this makes it difficult
to effectively apply Ranganathan's approach.
[0210] The FIR apodization scheme of the present invention offers a
way to maintain high resolution at the focus and expand the depth
of field during transmission. One version of the optimization
problem for computing the FIR filter weights is represented as:
min w S out w 2 subject to the quadratic constraint S in w 2 = 1 ,
( 24 ) ##EQU00015##
[0211] Our goal in expanding the transmit depth of field is not to
improve the contrast of a single cyst at the focus, but is rather
to enhance the contrast of a series of cysts located along the beam
line, but at differing ranges. If we consider a simple situation
with three cysts of interest then the propagation matrix for each
of these cysts can be represented as S.sub.1, S.sub.2, and S.sub.3.
Each of these propagation matrices can be manipulated to form
propagation matrices for the inside and outside of each of these
cysts. The overall propagation matrix considering the outer regions
of all the cysts is
S out = [ S 1 out S 2 out S 3 out ] . ( 25 ) ##EQU00016##
The overall propagation matrix considering the inner regions of all
the cysts is
S in = [ S 1 in S 2 in S 3 in ] . ( 26 ) ##EQU00017##
Substituting these expressions into equation (24) will solve for
the FIR filter weights that simultaneously optimize cystic point
contrast across the full set of cysts.
[0212] In medical ultrasound it is common that frequency dependent
attenuation reduces the amplitude of signals received from deeper
ranges. This effect can be taken into account by differentially
weighting the propagation matrices from the different cysts before
combining them. The cysts which have attenuated system responses
will typically need to be weighted more highly for the FIR filter
weights to be computed in a manner that fairly weights these
cysts.
Using FIR Apodization to Improve Robustness to Phase Aberration
[0213] Phase aberration, that is inhomogeneities in the speed of
sound of tissue, has long been considered a major limitation to
clinical ultrasound image quality. While the examples below will
show that the FIR apodization scheme of the present invention is
intrinsically robust to typical aberrations, the Quadratically
Constrained Least Squares FIR weight design method can be employed
to design weights that are even more robust to phase
aberrations.
[0214] If the statistical properties of typical phase aberrations
are known then it is possible to form a propagation matrix S for
each of a number or possible realizations of the phase aberration.
These system models can be concatenated to yield an overall
propagation matrix that captures the variability of the phase
aberrators and their impact on system performance. In one simple
case the propagation matrices would be formed from only three
aberrator realizations so that
S out = [ S 1 out S 2 out S 3 out ] and ( 25 ) S in = [ S 1 in S 2
in S 3 in ] . ( 26 ) ##EQU00018##
The FIR filter weights could then be determined using equation
(9).
[0215] To form highly robust weights one would likely employ dozens
or even hundreds of aberrator realizations, rather than the three
described above. Furthermore, the aberrator models might be
adjusted to incorporate amplitude aberration, or even spatially
distributed aberrations.
[0216] Phase aberrations not only reduce image contrast and
resolution, but because they often apply a linear phase tilt across
the array they tend to shift the image slightly in angle. Since the
image shift is not typically important it may be desirable to
ignore this effect when determining FIR filter weights to optimize
cystic contrast. This can be done by adjusting the center of each
mask used to form S.sub.in and S.sub.out so that it lies at the
apparent cyst center, after aberrator induced image shifting.
Applying FIR Apodization in DSIQ Beamforming
[0217] The Direct Sampled In-phase Quadrature (DSIQ) beamformer was
designed to be a low complexity, low power beamformer. It can be
used with very low complexity analog electronics and can implement
focusing using simple digital multiplication. Although it offers
significant advantages in terms of power consumption and system
complexity, DSIQ beamforming has generally been viewed as offering
relatively poor image quality because of intrinsic tradeoffs and
simplifying assumptions it incorporates. Application of the FIR
filter apodization scheme of the present invention can
significantly improve the performance of the DSIQ beamformer.
[0218] A key difference between the DSIQ beamformer and the other
beamformers considered in this disclosure is that the DSIQ
beamformer is optimized to form C-Scan images (image planes
parallel to the transducer face). As such, it does not form the
long time records (RF lines and A-Lines) that are typical for other
beamformers. However, as with other beamformers, envelope detection
must be performed to produce an image that can be interpreted by
users. This requires an alternate approach to envelope detection.
In the conventional DSIQ beamformer the output at each pixel
consists of a complex value, A+jB, where j=sqrt(-1). The magnitude
of the output image at that point (i.e. the envelope) is simply
computed as (A+jB)(A-jB)=A.sup.2+B.sup.2.
[0219] The most straightforward implementation of the DSIQ
beamformer with FIR weights is to simply assume that the DSIQ pairs
(i.e. samples acquired one quarter period apart) form a single
complex sample. In this situation the computed weights are also
considered complex and the design process is analogous to that used
for complex demodulated signals as described above. If we
incorporate a generic noise model (design following the robust
algorithm) then the problem can be stated mathematically as solving
the generalized eigenvalue problem given as:
(S.sub.out.sup.TS.sub.out+.sigma..sub.outR)w=.lamda.(S.sub.tot.sup.TS.su-
b.tot+.sigma..sub.loadR)w (27)
[0220] Where R R is the covariance function of the noise. This
expression will yield a set of FIR filter weights consistent with
the assumption that the DSIQ sample pairs are representative of an
underlying complex signal.
[0221] Although the above design process assumes that DSIQ pairs
are strictly equal to complex signals, they are not. To assume that
they are, and require simple complex weights, limits the potential
improvements available from the FIR beamformer and associated
weight design method. A varies of alternative design methods can be
employed to include more flexibility in the design and application
of the eights.
[0222] In one method of designing FIR filter weights for a DSIQ
beamformer, two sets of scalar weights are designed to generate two
outputs from the beamformer. An additional design goal is also
added to encourage orthogonality between the two outputs and
therefore make their combination appropriate for detection. One
method of encouraging this orthogonality is to make use of a second
propagation matrix, T, which is the axial Hilbert Transform of the
true propagation matrix S. Note that T must be orthogonal to S by
virtue of the application of the Hilbert Transform. It does not
however explicitly model any aspect of the system, but is rather a
mathematical construct used to induce orthogonality between the two
outputs (per pixel) of the DSIQ beamformer. Utilizing this
construct the FIR filter weight design problem becomes:
min w ( S out w 0 2 + S out w 1 2 + .gamma. Sw 0 - Tw 1 2 + E ( w 0
+ w 1 ) 2 ) ( 28 ) ##EQU00019##
subject to
.parallel.S.sub.inw.sub.0.parallel..sup.2+.parallel.S.sub.inw.sub.1.para-
llel..sup.2=1 (29)
[0223] The E term of this expression encompasses electronic noise.
Note that the noise term is not included in the constraint in this
particular case. The noise term may alternatively be included and
the resulting FIR filter weights will have a somewhat different
sensitivity to noise. Likewise, the constraint in this example uses
only the system model for the echoes originating from the inside of
the cyst. Alternatively the system model for the entirety of the
field might be used. Again, the solution will be somewhat different
but would fall within the scope of the present invention. The
solution of the above problem can be found via a generalized
eigenvalue problem of the form:
( [ S out T S out 0 0 S out T S out ] + .beta. [ S T S - S T T - T
T S T T T ] + .sigma. load [ R 0 0 R ] ) w = .lamda. ( [ S tot T S
tot 0 0 S tot T S tot ] ) w ( 30 ) ##EQU00020##
[0224] Alternatively the S and T terms can be selected to encompass
only the inner region of the cyst. The term B is a parameter
adjusted by the designer to determine the importance of
orthogonality between the two outputs of the beamformer. Other
methods of encouraging orthogonality between the outputs can also
be implemented. In equation (30), it should be recognized that the
term Represents the autocorrelation matrix of the noise represented
by E. FIG. 32 shows an integrated lateral beamplot 3200 for a
conventional DSIQ beamformer with SNR=5.8 dB, an integrated lateral
beamplot 3202 for a conventional DSIQ beamformer with SNR=1.3 dB,
an integrated lateral beamplot 3204 for an embodiment of a DSIQ
beamformer using designed FIR apodization according to the present
invention, SNR=0 dB, and an integrated lateral beamplot 3206 for an
embodiment of a DSIQ beamformer using designed FIR apodization
according to the present invention, SNR=1 B.
EXAMPLES
[0225] The following examples are put forth so as to provide those
of ordinary skill in the art with a complete disclosure and
description of how to make and use the present invention, and are
not intended to limit the scope of what the inventors regard as
their invention nor are they intended to represent that the
experiments below are all or the only experiments performed.
Efforts have been made to ensure accuracy with respect to numbers
used (e.g. amounts, temperature, etc.) but some experimental errors
and deviations should be accounted for. Unless indicated otherwise,
parts are parts by weight, molecular weight is weight average
molecular weight, temperature is in degrees Centigrade, and
pressure is at or near atmospheric.
Example 1
Comparing the FIR (Non-Robust) and the DAS Beamformers
[0226] A 64 element 150 .mu.m pitch 1D linear array operating at
6.5 MHz and 75% fractional bandwidth was simulated, using DELFI, a
custom ultrasound simulation tool (e.g., see Ellis et al., "A
Spline Based Approach for Computing Spatial Impulse Responses",
IEEE Trans. on Ultrason., Ferroelect., Freq. Contr., vol. 54, no.
5, pp. 1045-1054, 2007, which is hereby incorporated herein, in its
entirety, by reference thereto) that can be downloaded from the
Mathworks MATLAB (The Mathworks, Inc. Natick, Mass.) file exchange
website (mathworks.com/matlabcentral). All calculations were
performed on an IBM Intellistation Z Pro (Processor speed 2.80 GHz,
4.00 Gb RAM. IBM Corporation, Armonk, N.Y.).
[0227] Instantaneous spatial responses were calculated in a 2D
plane, azimuth and range, with a particular receive focus. Testing
was performed to show the ability of the tap weights (QCLS)
algorithm to produce optimal responses when using different FIR
filter tap lengths (i.e., tap length referring to the number of
taps used in a FIR filter) and different receive focal depths. FIR
filter tap lengths ranging from 1-tap to 13-taps were implemented
and the results of each were compared to ISR's produced using a
prior art DAS beamformer with conventional apodization functions
applied. In order to investigate the FIR beamformer 10 with
multiple taps 20T on each channel, multiple ISRs with different
receive foci were calculated. The receive focus of each ISR in the
FIR beamformer 10 was separated by 19.3 .mu.m in the axial
direction. Thirteen ISRs were acquired/calculated with receive foci
centered around a predetermined focal depth in order to calculate
the unique 1, 3, 5, 7, 9, 11, and 13-tap FIR filters 10. For
example, in order to calculate the tap weights 20 for the 3-tap 20T
FIR filters 18 for the FIR beamformer 10 with a receive focus at
2.0 cm, the receive element ISRs that had receive foci of 1.99807
cm, 2.00000 cm, and 2.00193 cm, respectively were used. Each ISR
was computed by spatial sampling by 20 .mu.m axially and 50 .mu.m
laterally over a large enough area to acquire the entire
response.
[0228] A cyst size was then specified. For example, a cyst size
having a 300 .mu.m radius was specified in one instance, in order
to identify the spatial points that lie outside the cyst and inside
the cyst to populate the ISR propagation matrices. Once the
propagation matrices ere populated, weights were calculated
according to the QCLS algorithm previously described.
[0229] As noted previously, cyst size is an important parameter in
the QCLS apodization design method: specifying the propagation
matrices in equation (8) and implicitly defining mainlobe size in
the resulting ISR. QCLS weights remains similar over a range of
cyst sizes. A set of FIR apodization weights was calculated to
achieve optimal contrast at every specified cyst size. FIG. 911
shows cystic point contrast curves for the 5-tap FIR beamformer 10
with a receive focus at 2.0 cm (also the transmit focus). Cystic
contrast was computed using equation (8) with the ISR centered in
the middle of the cyst and plotted as a function of cyst size (from
0.1 mm to 1.0 mm in radius). The dashed line 802 represents the
cystic contrast lower bound for this particular beamformer 10 at
the stated receive focal depth (i.e., 2.0 cm). This lower bound is
constructed by calculating cystic contrast with the optimal
apodization profile at each cyst size. The contrast curves for the
5-tap QCLS apodization profiles 804, 806, 808 corresponding to a
design cyst radius of 100 .mu.m, 500 .mu.m, and 1000 .mu.m,
respectively. For each design cyst radius, the contrast curse 804,
806, 808 touches the lower bound 802 at that cyst size, and
contrast performance suffers away from the design cyst size.
[0230] It has been determined that the QCLS profile around the
"knee" of the lower bound curve 802 offers good performance over a
large working range of cyst sizes. For example, in FIG. 911 the 500
.mu.m contrast curve 806 achieves better contrast than the 1000
.mu.m curve 808 for the smaller cost sizes and also outperforms the
100 .mu.m curve 804 for the larger cyst sizes. The 100 .mu.m and
1000 .mu.m curves 804, 808 shown that operating at the extremes
(the relatively smallest cyst sizes or the relatively largest cyst
sizes) will produce optimal contrast at the specific small or large
design cyst size, but performance is seriously degraded at other
cyst sizes out of the either extremely small or extremely large
range. For the remainder of the simulations, a 400 .mu.m design
cyst radius was used for the QCLS profiles unless otherwise
noted.
[0231] As a result of the comparisons, it was determined that
significant improvements in contrast resolution can be achieved
with the FIR beamformer 10 using a modest filter tap length. FIG.
1012 shows cystic point contrast curves for the DAS beamformer 1000
and FIR beamformer 10 with a receive focus at 2.0 cm. The dashed
vertical line 902 shows the design cyst radius. Cystic contrast
curves 904, 906 and 908 are plotted for the DAS beamformer 1000
with Rectangular window, Hamming window, and Nuttall window
apodization functions respectively, using a range of cyst sizes to
compare performance with the results of the FIR beamformer using
weights calculated for a 400 .mu.m design cyst. Cystic contrast
curves 910, 912, 914, 916, 918, 920 and 922 are plotted for the FIR
beamformer 10 having 1-tap, 3-tap, 5-tap, 7-tap, 9-tap, 11-tap, and
13-tap length FIR filters 18, respectively, using 400 .mu.m design
cyst radius. Data were calculated from the ISRs focused at 2.0 cm
on transmit (f/2) and 2.0 cm on receive (f/2). It can be observed
from FIG. 1012 that for the particular criteria stated above, both
the Hamming (see contrast curve 906) and Nuttall (se contrast curve
908) windows degraded the cystic contrast compared to the
rectangular window (see contrast curve 904). In those cases, the
reduction in sidelobe energy achieved through apodization did not
outweigh the increase in mainlobe size of the resultant ISR. The
FIR beamformer 10 employing a FIR filter 18 having seven taps 20T
(i.e., 7-tap FIR beamformer, see contrast curve 916) improved
cystic contrast by almost 20 dB and the 13-tap FIR beamformer (see
contrast curve 922) improved contrast by almost 25 dB.
[0232] As noted, for the specifications and operating conditions
noted above, the conventional receive Hamming window and Nuttall
window apodization functions used in the DAS beamformer 1000
performed worse than flat apodization (i.e., using a rectangular
window). Although the Hamming and Nuttall ISRs had lower sidelobes,
the cystic resolution metrics showed that the lower sidelobes did
not outweigh the resulting increase in mainlobe width. The 1-tap
QCLS profile on the other hand lowers sidelobe levels, maintains a
narrow mainlobe, and outperforms all the conventional apodization
functions for a large range of cyst sizes, as shown by the
resultant contrast curve 910. More compelling were the dramatic
increases in cystic resolution when using the multi-tap FIR
beamformer 10. The 3-tap FIR beamformer 10 improved contrast
resolution by 10 dB (i.e., compare contrast curve 912 to contrast
curve 904), the 5-tap by 15 dB, the 7-tap by 20 dB, and the 9-tap
by more than 25 dB. Using even longer tap lengths (11 and 13)
improved contrast a few more dB over the 9-tap curve but suggested
that there is a limit to the increase in cystic contrast achievable
by the FIR beamformer, and showed diminishing returns in the
incremental amount of increase in cystic contrast.
[0233] In order to show the effects of receive focal depth on the
FIR beamformer 10 relative to the DAS beamformer 1000 using a
rectangular windows. FIGS. 11A-11C13A-13C show integrated lateral
beamplots, FIGS. 11D-11F13D-13F show plots of cystic contrast vs.
cyst size, and FIGS. 11G-11I13G-131 show plots of cystic contrast
vs. receive channel signal to noise ratio (SNR) curves comparing
different apodization functions at different dynamic receive focal
depths (1.0 cm, 2.0 cm and 3.0 cm, respectively, with transmission
(Tx) focus fixed at 2.0 cm). The FIR-QCLS tap weights were
calculated for 1-tap, 3-tap, 5-tap, and 7-tap FIR filters 18 with a
design cyst radius of 0.4 mm (indicated bid the dashed vertical
line 1021 in the beamplots of FIGS. 11A-11C13A-13C and in the
cystic contrast vs. cyst size plots of FIGS. 11D-11F), 13D-13F). A
large reduction in sidelobe levels of the plots in FIGS.
11A-11C13A-13C can be seen in the plots 1024, 1026 and 1028 for the
higher tap-length filters.
[0234] FIGS. 11D-11F13D-13F show GCR metric curves plotting cystic
contrast as a function of cyst radius given infinite channel SNR
for the simulated 2D ISRs. Cystic contrast is improved by more than
20 dB for the higher tap FIR filters at dynamic receive focal
depths of 1.0 and 2.0 cm (e.g., see 1034, 1036 and 1038 in FIGS.
11D13D and 11E13E, indicating contrast curves for 3-tap FIR filter.
5-tap FIR filter and 7-tap FIR filter, respectively). In general
longer tap filters increasingly improve contrast resolution. FIGS.
11G-11I13G-13I shown plots of GCR metric curves at a constant cyst
radius (i.e., 0.4 mm cyst radius, which was the design cyst size).
These plots show how robust the beamformers 10 are to varying
levels of electronic noise. Notice that in general the performance
of the longer tap-length FIR filters (e.g., see plots 1044, 1046
and 1048 representing 3-tap, 5-tap and 7-tap FIR filters,
respectively) rapidly decreases in the presence of noise compared
to the rectangular DAS beamformer represented by plot 1040. The
single tap FIR filter, represented bad plot 1042, also did not
perform as well as tie longer tap-length filters. In reasonable SNR
environments (between 30 and 40 dB) the 3-tap FIR-QCLS beamformer
10 (plot 1044) offers significant gains in contrast resolution
compared to the rectangular apodized DAS beamformer 1000 (plot
1040).
[0235] The results reported in FIGS. 13A-13I were calculated in
regard to a 64 element receive aperture dynamically focused at 1.0
cm (FIGS. 13A, 13D and 13G), 2.0 cm (FIGS. 13B, 13E and 13H), and
3.0 cm (FIGS. 13C, 13F and 13I). For these simulations the transmit
focus was fixed at 2.0 cm. FIGS. 13A-13C plot the integrated
lateral beamplots when using different apodization windows. The
beamplots were calculated by integrating the energy of the ISRs in
range. The FIR-QCLS windows were compared against conventional
windows such as the rectangular, Hamming, and Nuttall windows. The
results of FIGS. 13A-13I are shown only for the QCLS windows of the
present invention compared with the prior art rectangular window,
since the Hamming and Nuttall windows performed worse than the
rectangular window at all receive depths. FIR-QCLS windows were
calculated using a design cyst radius of 0.4 mm with 1-tap, 3-taps,
5-taps, and 7-taps per channel.
[0236] Notice the marked reduction of the sidelobe levels for the
higher tap length FIR-QCLS beamplots (e.g., plots 1024, 1026 and
1028). Some lateral beamplots show sidelobe level reduction of 30
dB compared to the beamplot for a rectangular window. With regard
to FIGS. 13D-13F, it can be noted that, in general, contrast
improves when increasing the number of taps on each receive
channel; however the biggest jump in contrast improvement occurred
between one and three taps (compare 1032 with 1034). The GCR metric
cures of FIGS. 13G-13I, which plot cystic resolution as function of
receive channel input SNR, indicate a tradeoff in beamformer
sensitivity and increased contrast resolution performance when
using the basic FIR beamformer 10 that does not include the
features of the robust beamformer embodiments described above.
Compared to the rectangular DAS beamformer (see plot 1040), the
multi-tap FIR beamformer's 10 cystic resolution performance
degrades more rapidly in the presence of noise. However, given a
reasonable input channel SNR between 30 and 40 dB, the 3-tap FIR
beamformer (plot 1044) offers more than 10 dB improvement in
contrast resolution than the DAS beamformer (plot 1040) at receive
depths of 1.0 and 2.0 cm. The SNR performance of the FIR beamformer
10 is discussed further herein.
[0237] FIG. 1214 shows the calculated FIR-QCLS weights for the data
dynamically focused at 2.0 cm. These weights were computed for a
design cyst radius of 0.4 mm. The 1-tap and 3-tap FIR-QCLS weights
1100 and 1102, respectively, are mostly smooth Gaussian like
functions across the aperture, except at the endpoints where
discontinuities appear. The 5-tap and 7-tap weights 1104 and 1106,
respectively, are much more variant and discontinuous. It is
interesting to note that some FIR-QCLS weights took on negative
values, a phenomenon never seen in conventional windows like the
Hamming or Nuttall window. The sign of the weight values also
inverted in time on some channels as seen in the middle or the
array for the 5-tap and 7-tap filters. Although the weights
computed from the FIR-QCLS algorithm were always real, this
inversion in time suggests that a 180.degree. phase shift between
consecutive time samples reduces sidelobe energy in the ISR.
[0238] FIG. 1315 shows the magnitude and phase response for the
3-tap, 5-tap and 7-tap FIR filters represented in FIG. 12, 14.
Plots 1202, 1206 and 1210 show magnitude responses for the 3-tap,
5-tap and 7-tap FIR filters, respectively and plots 1204, 1208 and
1212 show phase responses for the 3-tap, 5-tap and 7-tap FIR
filters, respectively.
[0239] The responses shown in FIG. 1315 illustrate that, in
general, the FIR filters are high pass, and that the cutoff
frequency shifts higher as tap length increases. The phase response
for the filters is in general nonlinear, and the responses become
more discontinuous as tap length increases. Intuitively the high
pass characteristics of the FIR filters make sense. The QCLS
algorithm forces narrow mainlobes, which necessitates using the
high frequency components in the signal. The filters frequency
response is one reason for the degraded SNR performance of the FIR
beamformer seen in FIGS. 11G-11I.13G-13I. The center frequent of
the simulated transmitted pulse was 6.5 MHz and the cutoff
frequency for the 7-tap FIR filters is around 7 MHz.
Example 2
Performance of the Non-Robust FIR Beamformer in the Presence of
Phase Aberration
[0240] Receive channel focal delays 1002 in the prior art DAS
beamformer 1000 are calculated assuming a propagation speed of
sound in tissue. Conventional systems assume a uniform sound
velocity of 1540 m/s, however actual sound velocities in human
tissue vary between human subject and tissue type. Spatial
variations from the assumed sound speed cause wavefront distortion,
amplitude variation, and phase variation of the ultrasound beam.
These distortions or phase aberrations adversely affect the quality
of in vivo images. Phase aberration will distort the DAS
beamformer's 1000 ISR, reducing the contrast and resolution of the
output image.
[0241] Recent literature indicates that phase aberrations in the
human breast can be modeled as a nearfield thin phase screen
characterized by a root mean square (RMS) amplitude strength of 28
ns and a full-width at half-maximum (FWHM) correlation length of
3.6 mm. A series of simulations were performed wherein aberrations
were used to distort the ISR formed by the FIR beamformer 10.
Specifically data from 100 realizations of a one-dimensional
aberrator were used to get good statistics. To construct the
aberrators, 100 random processes were generated with an a priori 28
ns RMS strength and an a priori 3.6 mm FWHM correlation length.
Some of the 100 aberrators were thus stronger or weaker than the 28
ns RMS and 3.6 mm FWHM a priori characteristics. The 100
aberrators' mean RMS value was 27.7 ns with a standard deviation of
9.8 ns and the 100 aberrators' mean FWHM value was 3.7 mm with a
standard deviation of 1.7 mm. Each aberrator acted to alter the
instant in time at which each receive channel's spatial response
was calculated. Note that the same aberration would apply to all
the ISRs required for the input into the FIR beamformer 10.
[0242] FIGS. 14A-14N16A-16N show unaberrated and aberrated
simulated ISRs for different apodization functions, with FIGS.
14A-14B16A-16B showing unaberrated and aberrated simulated ISRs
1300, 1302, respectively for a rectangular window function used to
apodize signals received by a DAS beamformer 1000, FIGS.
14C-14D16C-16D showing unaberrated and aberrated simulated ISRs
1304, 1306, respectively for a Hamming window function used to
apodize signals received by a DAS beamformer 1000. FIGS.
14E-14F16E-16F showing unaberrated and aberrated simulation ISRs
1308, 1310, respectively for a Nuttall window function used to
apodize signals received by a DAS beamformer 1000, FIGS.
14G-14H16G-16H showing unaberrated and aberrated simulated ISRs
1312, 1314, respectively for a 1-tap QCLS apodization function used
to apodize signals received by a 1-tap FIR beamformer 10, FIGS.
14I-14J16I-16J showing unaberrated and aberrated simulated ISRs
1316, 1318, respectively for a 3-tap QCLS apodization function used
to apodize signals received by, a 3-tap FIR beamformer 10. FIGS.
14K-14L16K-16L showing unaberrated and aberrated simulated ISRs
1320, 1322, respectively for a 5-tap QCLS apodization function used
to apodize signals received by a 5-tap FIR beamformer 10, and FIGS.
14M-14N16M-16N showing unaberrated and aberrated simulated ISRs
1324, 1326, respectively for a 7-tap QCLS apodization function used
to apodize signals received by a 7-tap FIR beamformer 10.
[0243] All images In FIGS. 14A-14N16A-16N are of a 6 mm (lateral)
by 2 mm (axial) area of the ISR. The absolute value of each ISR was
calculated and then log compressed to 60 dB for visualization. The
aberration profile 1330 (3.6 mm FWHM, 28.8 ns RMS) associated with
this particular realization is shown in FIG. 14O.16O. The
aberration distorts the mainlobe and raises sidelobe levels in all
ISRs. Note that the FIR beamformer ISRs maintain relatively narrow
mainlobes. The sidelobe energy in the aberrated FIR beamformer ISRs
continually decreases as tap length increases.
[0244] FIGS. 14A-14N16A-16N show how the simulated ISRs for
different receive apodizations are affected by phase aberration.
For each apodization function, the top figure shows the unaberrated
2D ISR with a receive focus of 2.0 cm and the bottom figure shows
the same ISR that has been aberrated. The 0.4 mm design cyst radius
QCLS apodization profiles were used for all FIR beamformer ISRs. It
is clear that the aberrator raises sidelobe levels and distorts the
mainlobe for every ISR. It is interesting that the FIR beamformer
ISRs maintain a narrow mainlobe and low sidelobe levels even in the
presence of aberration. Furthermore, the sidelobe energy in the
aberrated FIR beamformer ISRs continually decreases as tap length
increases. Although the absolute degradation between the
unaberrated and aberrated ISRs for the FIR beamformer is more than
the DAS beamformer, the aberrated ISRs for the multi-tap FIR
beamformer still have lower sidelobes and tighter mainlobes than
the unaberrated DAS beamformer ISRs. These results suggest that the
FIR beamformer is robust to errors in the model induced by moderate
phase aberrations.
[0245] The linear component of any given aberrator realization will
act to steer the ultrasound beam laterally from its intended focus.
In order to be consistent when applying the resolution metric,
cystic contrast was computed after re-centering the cyst at the
maximum of each aberrated ISR. This resulted in a constant measure
or the point contrast of the center of the cyst in the final output
image, but assumed shift invariance of the aberrated ISR over a
small range. FIG. 1517 summarizes the effects of aberration on the
contrast curves of the DAS beamformer 1000 and FIR beamformer 10.
FIG. 1517 shows plots of the unaberrated and aberrated cystic point
contrast curves for the rectangular (1402 and 1404, respectively)
and 7-tap (1406 and 1408, respectively) ISRs in the absence of
noise. Also shown is the lower bound (LB) contrast curve 1410 for
the 7-tap FIR beamformer 10, which was calculated by using the
optimal FIR-QCLS profile at each cyst size. The errorbars 1412 show
+/-1 standard deviation about the mean values of 1402 and errorbars
1414 show +/-1 standard deviation about the mean values of 1414.
Aberration degrades the cystic point contrast performance for both
apodization functions: the 7-tap ISR by 7 dB and the rectangular
ISR by 2 dB. However, the 7-tap aberrated FIR beamformer
outperformed the unaberrated rectangular DAS beamformer by 10 dB.
The Hamming and Nuttall window functions performed worse than the
rectangular window function and are therefore not shown in this
plot for clarity.
[0246] FIGS. 16A-16C18A-18C shows plots of the mean cystic contrast
for each aberrated ISR relative to the rectangular window. The 0 dB
point on the y-axis in each plot indicates the aberrated
rectangular window's mean cystic contrast for each cyst size. A
more positive dB value indicates better performance than the
rectangular window, and errorbars are +/-1 standard deviation. Each
of FIGS. 16A-16C18A-18C show the Hamming 1502, Nuttall 1504 and
1-tap 1506 plots, with FIG. 16A18A additionally showing the 3-tap
plot 1508, FIG. 16B18B additionally showing the 5-tap plot 1510 and
FIG. 16C18C additionally showing the 7-tap plot 1512, in order to
reduce clutter. The Hamming and Nuttall windows achieved worse
cystic point contrast (1502 and 1504, respectively) compared to the
rectangular window over nearly the entire range of investigated
cyst sizes. The 1-tap QCLS weights in the presence of aberration
still improve contrast (see plot 1506) for the smaller cyst sizes
but perform worse than the rectangular Hamming, and Nuttall windows
for the large diameter cysts. This is to be expected given the 0.4
mm design cyst radius.
[0247] It can be seen that contrast continuously improves with
longer tap-length filters, and the 7-tap QCLS weights (plot 1512)
maintain 10-15 dB cystic point contrast improvements compared to
the rectangular window for a large range of cyst sizes. These
results show that the FIR beamformer 10 is robust to relatively
strong phase aberration errors. Furthermore even the aberrated FIR
beamformer 10 would outperform the perfectly phase corrected DAS
beamformer 1000. These simulation results suggest that the FIR
beamformer 10 can dramatically improve the contrast resolution of
ultrasound images and is robust in the presence of phase
aberration.
Example 3
Application to an Ultrasonic Scanning System
[0248] An embodiment of the beamformer 10 according to the present
invention was applied to an existing ultrasound scanner to improve
the spatial response characteristics thereof. The ultrasonic
scanner system used was the Ultrasonix Sonix RP ultrasound scanner
(Ultrasonix Medical Corp., Richmond, BC, Canada). The Sonix RP
system has a software development kit (SDK) named TEXO that enables
low level scanner control with the ability to acquire single
channel RF data sampled at 40 MHz with 12 bit precision. The
present inventors created an interface to the TEXO SDK using
PYTHON.TM. programming language that allowed creating of customized
pulse sequences without the need to recompile the system C code.
Utilizing the PYTHON.TM. interface with the TEXO SDK a full set of
synthetic receive aperture data was acquired from a 64 element
transmit aperture and 64 element receive aperture in fractions of a
second. In order to measure the 2D ISR required for the inventive
algorithm, a 20 .mu.m diameter steel wire in a tank full of
deionized water was imaged. The transmit aperture of the system was
electronically scanned across the array while mechanically moving
the array using a 3-axis positioning system (Newport Motion
Controller MM3000, Newport Co., Irvine, Calif.) in order to achieve
azimuthal spatial sampling of 75 .mu.m and axial spatial sampling
of 50 .mu.m. The data was interpolated using MATLAB, using cubic
splines to achieve 25 .mu.m azimuthal sampling and 12.5 .mu.m axial
sampling. A 1.95 cm (azimuth) was acquired by 0.2 cm (range) by
3000 time sample dataset to characterize the 3D spatio-temporal
PSF. The entire experiment required 29 hours to execute, resulting
in over 10 Gbytes of raw, averaged RF data. The water temperature
remained relatively constant over the course of the experiment,
ranging between 21.6-22.4.degree. C.
[0249] An L14-5/38 128 element linear array probe was used and was
excited with a 1 cycle 6.67 MHz pulse. The transmit aperture
consisted of 64 elements focused at 4.0 cm in range (f/2). 64
receive elements were acquired synthetically and each receive
signal was averaged 100 times to improve electronic SNR. The
receive data was digitally bandpass filtered in MATLAB using a
101.sup.st order bandpass filter with cutoff frequencies at 4 and 8
MHz. An experimental 2D ISR was formed by sampling the interpolated
3D spatio-temporal PSF for each receive element according to a
dynamic receive focusing profile for a particular receive
focus.
[0250] The log compressed, envelope detected experimental ISRs
dynamically focused at 2.0 cm are shown in FIG. 17.19, ISRs are
shown for conventional apodization functions (rectangular window
function 1602, Hamming window function 1604 and Nuttall window
function 1606) and 1-tap 1608, 3-tap 1610, 5-tap 1612 and 7-tap
1614 FIR-QCLS windows designed for a cyst radius of 0.35 mm. The
cyst 1616 having the design cyst radius is shown for reference. All
images are log compressed to 70 dB. Notice the progressive
reduction of ISR energy in the sidelobe regions when using the
multi-tap FIR-QCLS design. The 7-tap FIR-QCLS ISR 1614 has superior
axial and lateral resolution compared to the other ISRs.
[0251] FIGS. 18A-18C20A-20C show the experimental integrated
lateral beamplots (FIG. 18A20A) and GCR metric curves. The FIR-QCLS
weights reduce sidelobe levels of the ISR plots 1708, 1710 for
3-tap and 7-tap algorithms, respectively, lower the total ISR
energy outside the mainlobe, and decrease mainlobe width relative
to the ISRs of beamplots 1702, 1704 and 1706 produced using
conventional Rectangular, Hamming and Nuttall window algorithms,
respectively. For clarity, only the 3-tap and 7-tap QCLS plots are
shown. The contrast curves 1712, 1714, 1716, 1718 and 1720 assuming
infinite SNR for the rectangular, Hamming, Nuttall, 3-tap QCLS and
7-tap QCLS experimental ISRs, respectively, are shown in FIG.
19B.20B. The FIR-QCLS ISRs show increases in cystic resolution
compared to the conventional windows. Specifically, the 7-tap
apodization profile improved contrast 1720 by 7 dB compared to the
Hamming window 1714, by 10 dB compared to the rectangular window
1712, and by 12 dB compared to the Nuttall window 1716 over a range
of cyst sizes. Furthermore, the 7-tap curve 1720 achieves the best
contrast for all cyst sizes investigated. The SNR performance GCR
metric curves 1722, 1724, 1726, 1728 and 1730 for the rectangular,
Hamming, Nuttall, 3-tap QCLS and 7-tap QCLS experimental ISRs,
respectively, are shown in FIG. 18C.20C. These results reinforce
the tradeoff in SNR and cystic resolution with the FIR beamformer
(that does not include the robust design) seen in the
simulations.
[0252] The QCLS weights for the multi-tap FIR filters are shown in
FIG. 19.21. These weights correspond to the ISRs dynamically
focused at 2.0 cm in FIG. 17.19. The weights shown similar
characteristics to the simulations: smooth curves across the
aperture, discontinuities at the edges of the aperture, and sign
inversion in time. That is, the 1-tap and 3-tap FIR-QCLS weights
1800 and 1802, respectively, are mostly smooth Gaussian like
functions across the aperture, except at the endpoints where
discontinuities appear. The 5-tap and 7-tap weights 1804 and 1806,
respectively, are much more variant and discontinuous. It is
interesting to note that some FIR-QCLS weights took on negative
values, a phenomenon never seen in conventional windows like the
Hamming or Nuttall window. The sign of the weight values also
inverted in time on some channels as seen in the middle of the
array for the 5-tap and 7-tap filters. Although the weights
computed from the FIR-QCLS algorithm were always real, this
inversion in time suggests that a 180.degree. phase shift between
consecutive time samples reduces sidelobe energy in the ISR.
[0253] FIG. 2022 shows the magnitude and phase response for the
3-tap, 5-tap and 7-tap FIR filters represented in FIG. 19.21. Plots
2002, 2006 and 2010 show magnitude responses for the 3-tap, 5-tap
and 7-tap FIR filters, respectively, and plots 2004, 2008 and 2012
show phase responses for the 3-tap, 5-tap and 7-tap FIR filters,
respectively.
[0254] The responses shown in FIG. 2022 illustrate that, in
general, the FIR filters are high pass, and that the cutoff
frequency shifts higher as tap length increases. Much like the
simulation results in FIG. 1315, the experimental FIR filters are
in general high pass with increasing cutoff frequency as the tap
length increases. The phase response for the experimental filters
is nonlinear, but is not as discontinuous as the simulation phase
responses.
Example 4
Lesion Detectability
[0255] According to the simulation and experimental results, the
FIR beamformer 10 designed without using the robust methodology
improves cystic contrast but degrades echo SNR. Results from the
cystic resolution metric will not necessarily translate to improved
lesion detectability, in B-mode images, since the metric only
specifies the point contrast at the center of the cyst. Therefore
it is desirable to analyze detectability in B-mode images. B-mode
ultrasound images were simulated and a contrast to noise ratio
(CNR) was calculated. The CNR is defined as:
CNR = 10 log 10 ( I cyst I speckle ) , ( 28 ) ##EQU00021##
I.sub.cystI.sub.speckle where I.sub.cyst and I.sub.speckle are the
mean signal intensity values for image regions inside the cyst and
outside the cyst, respectively. B-mode images of cysts embedded in
a speckle generating background were simulated by performing a
2-dimensional convolution of a target function and an experimental
ISR. Note that this assumed spatial and temporal shift invariance
of the ISR over the image region, which was a reasonable assumption
over the small, simulated axial and lateral ranges. 1000 different
speckle generating backgrounds were simulated to get good
statistics on lesion contrast as computed by equation (11). B-mode
images of cyst sizes ranging from 0.1 mm to 1.75 mm in radius were
formed using the rectangular, Hamming, Nuttall, 1-tap QCLS, and
7-tap QCLS experimental ISRs (see FIG. 19). A representative
realization of the simulated B-mode images for all the different
ISRs is shown in FIGS. 21A23A (image 2002 using the rectangular
experimental ISR), 21B23B (image 2004 using the Hamming
experimental ISR), 21C23C (image 2006 using the Nuttall
experimental ISR), 21D23D (image 2008 using the 1-tap experimental
ISR) and 21E23E (image 2010 using the 7-tap experimental ISR). All
images 2002, 2004, 2006, 2008 and 2010 were envelope detected and
log compressed to 40 dB. These images show a 5 mm by 5 mm region
surrounding a 0.5 mm radius cyst. The QCLS weights were designed
for a 0.35 mm radius. The cyst in the image 2002 made using the
rectangular apodized ISR is corrupted with clutter from the
response's high sidelobes. The speckle size is finer than the other
images due to the ISR's narrow mainlobe. The Nuttall image 2000 has
much larger speckle size due to the large mainlobe width of the
response, which severely blurs the cyst. The Hamming 2004 and the
1-tap QCLS 2008 ISRs produced similar images, with the 1-tap ISR
arguably reducing the clutter inside the cyst to a greater degree.
The 7-tap ISR image 2010 clearly outperformed all the conventional
windows reducing clutter inside the cyst and sharpening the cyst
boundary. The actual size and shape of the cyst 2010 is shown in
FIG. 23F for comparison.
[0256] FIGS. 24A-24B plot cyst CNR computed from equation (11) as a
function of cyst radius, by using one thousand different images for
each cyst size. The images in FIGS. 23A-23E are just one
realization with one cyst size. The mean CNR values are plotted in
FIGS. 24A-24B, as computed over the 1000 trials. A more negative
contrast value indicates better performance. FIG. 24A shows plots
2102, 2104, 2106, 2108, 2110 corresponding to a computed contrast
at a cyst size that is the same size as the imaged cyst (100% plot)
for the rectangular image 2002, Hamming image 2004, Nuttall image
2006, 1-tap image 2008 and 7-tap image 2010, respectively. FIG. 24B
shows plots 2112, 2114, 2116, 2118, 2120 corresponding to a
computed contrast assuming a smaller cyst size than the imaged cyst
(70% plot) for the rectangular image 2002, Hamming image 2004,
Nuttall image 2006, 1-tap image 2008 and 7-tap image 2010,
respectively. The smaller cyst size is assumed for the computations
reported by plots in FIG. 24B in order to reduce edge effect
corruption in the CNR calculations. Contrast improved with
increasing cyst radius for all windows. Computing contrast with the
true cyst size resulted in a 2 dB improvement in B-mode CNR for the
7-tap response. Computing contrast with 70% of the true cyst size
resulted in a 4-10 dB CNR improvement for the 7-tap response over
the conventional windows. These results reinforce the qualitative
improvements seen in the B-mode images of FIG. 23D relative to
FIGS. 23A-23C.
Example 5
Robust FIR Beamforming
[0257] Comparisons were made between the imaging performances of
two beamforming architectures according to the present invention an
SMF beamformer 1150 and the conventional delay-and-sum beamformer
1000. Simplified depictions of all the different beamformers are
shown in FIGS. 25A-25D. FIG. 25A shows a conventional DAS
beamformer 1000 like that described above with regard to FIG.
1.
[0258] FIG. 25B illustrates a FIR beamformer 10 like that described
in regard to FIG. 2 above. Note that although only three taps per
filter are shown in FIG. 25B, that this is for illustration
purposes only and that the number of taps may be varied in the same
manner as described above. FIR beamformer 10 is referred to here as
a "dynamic focus" FIR beamformer as the FIR filters 18 are
spatially and temporally variant, and can be updated for each
output pixel in the final image.
[0259] The spatial matched filter (SMF) beamformer 1150 shown in
FIG. 25D also uses spatially and temporally variant FIR filters
1158 on each receive channel 16. The filters 1158 of the SMF
beamformer 1150 focus the incoming RF data While the SMF beamformer
1150 does not require any delay lines, the filters 1158 must be
long enough to account for the pulse length and delay curvature of
the returning echoes. The filter weights for both beamformers are
independent of the receive echoes: hence these beamformers are not
adaptive.
[0260] The "group focus" FIR beamformer 10' shown in FIG. 25C does
not dynamically focus the RF data at each filter tap 20T. For
example, the 3-tap 20T FIR filters 18 of the dynamic focus FIR
(DF-FIR) beamformer 10 in FIG. 25B provide as outputs three
different dynamic receive foci in one output sample. In contrast,
the RF data for all the channel taps 20T of a FIR filter 18 in the
beamformer 10' have the same one fixed receive focus. A simplified
schematic of beamformer 10' is shown in FIG. 25C, and referred to
as a "group focus" FIR (GF-FIR) beamformer. The group focus stage
is required to apply the same receive focal delay profile to
multiple samples on each channel. For the 3-tap example of FIG.
25C, this means that three consecutive samples of RF data all with
the same dynamic focal delay are used to create one output sample.
The tap length and filter weights of the GF-FIR beamformer 10' are
tunable parameters. The weights for the DF-FIR beamformer 10 and
GF-FIR beamformer 10' are computed using the robust QCLS
apodization design algorithm, whereas, the SMF beamformer weights
theoretically maximize the beamformer's output SNR in the presence
of white noise.
[0261] To perform the comparisons, a 64 element, one-dimensional
linear array 2 operating at 6.5 MHz and 75% fractional bandwidth
was simulated in DELFI, and nine instantaneous spatial responses
were measured in the azimuth-range plane. Each ISR had a different
receive foci separated in range by 19.3 .mu.m (equivalent to a 40
MHz filter sampling rate assuming a sound speed of 1540 m/s). These
ISRs were required to calculate the unique 1, 3, 5, 7, and 9-tap
FIR filters 18 for the DF-FIR beamformer 10 with a transmit focus
at 2 cm (f/2) and a receive focus at 1.0 cm (f/1).
[0262] A different set of spatial responses was simulated in order
to characterize the SMF beamformer 1150. The simulated acoustic
pulse was 47 samples in length at 40 MHz sampling, so 47 spatial
responses for each receive channel separated in time by 25 ns were
acquired. These ISRs all had a receive focus of 1.0 cm but were
measured at different instants in time. A spatial matched filtered
single element response was formed by multiplying each receive
channel ISR with the associated temporal acoustic pulse sample and
then summing all the 47 spatial responses in time. The ISRs for the
SMF beamformer 1150 were prefocused in order to save computation
time and memory. Prefocusing does not change the output of the SMF
beamformer 1150. The 47 ISRs originally computed for each receive
channel were also used for the GF-FIR beamformer 10'. Due to memory
constraints When implementing the QCLS algorithm, the longest
filters investigated for the DF-FIR 10 and GF-FIR beamformer 10'
were 9 taps 20T.
[0263] When computing the optimal QCLS apodization weights for the
two FIR beamformers 10 and 10', a range of design cyst radii from
0.1 mm to 1.0 mm as used. QCLS apodization profiles were also
computed for a range of .sigma..sub.design.sup.2 values from the
optimal CR window to the optimal SNR window, so that these two
design parameters (.sigma..sub.design.sup.2 channel SNR) and design
cyst radius) could be used to construct the robust FIR-QCLS
filters. Once these filters were constructed, their cystic
resolution performance as a function of cyst size and robustness to
noise as a function of receive channel input SNR
(.sigma..sub.load.sup.2) were quantified. All channel SNR values
were calculated based on the middle element of the receive aperture
in the DAS beamformer 1000.
[0264] FIGS. 26A-26B show the design SNR-CR curves for the DF-FIR
beamformer 10 as well as the CR performance of the rectangular
apodized DAS beamformer 1000, the SMF beamformer 1150, and five
different 9-tap DF-FIR beamformers 10. FIG. 26A shows the SNR-CR
design curves 2400, 2402, 2404, 2406 and 2408 for the 1-tap, 3-tap,
5-tap, 7-tap, and 9-tap DF-FIR beamformers 10, respectively, each
with a receive focus of 1.0 cm and a design cyst radius of 0.4 mm.
Note that design receive channel SNR (.sigma..sub.design.sup.2) was
varied from infinity to -40 dB. Each point along each of these
design curves is associated with a different set of FIR filters 18.
The wavy contour of the design curves arises from the eigenvalue
spread of the R.sub.tot matrix. As tap length increases the curves
become smoother. As filter tap length increases, the potential
cystic resolution performance increases. FIG. 26B shows the CR
curves 2410, 2412, 2414, 2416, 2418, 2420 and 2422 as a function of
receive channel SNR for the rectangular apodized DAS 1000, SMF
1150, and five 9-tap DF-FIR 10 beamformers at a design cyst radius
of 0.4 mm and receive focus of 1.0 cm, respectively. The SNR-CR
design curve 2424 is shown and the operating points for the five
different SNR constrained 9-tap DF-FIR beamformers are marked at
2430, 2432, 2434, 2436 and 2438, respectively, along curve 2424.
From FIG. 26B it can be seen that the SMF beamformer 1150 offers
2-3 dB (gains in cystic resolution and increased sensitivity
performance compared to the rectangular apodized DAS beamformer
1000. The optimal CR 9-tap DF-FIR beamformer (i.e., see 2438)
improves CR by more than 20 dB but its performance starts to
degrade when channel SNR approaches 70 dB. The optimal SNR 9-tap
DF-FIR beamformer 10, has worse CR performance than the DAS 1000
and SMF 1150 beamformer but better SNR performance. Using the 9-tap
DF-FIR beamformer 10 designed for 20 dB channel SNR offers 15 dB
improvement in CR and has a similar SNR performance to the DAS 1000
and SMF 1150 beamformers. Note that in high SNR environments it
makes sense to use the 9-lap DF-FIR beamformer 10 designed for 40
dB channel SNR, or in worse SNR environments to use the 9-tap
DF-FIR beamformer 10 designed for 0 dB channel SNR.
[0265] FIGS. 27A-27B show the design SNR-CR curves for the GF-FIR
beamformer 10' as well as the CR performance of the rectangular
apodized DAS beamformer 1000, the SMF beamformer 1150, and three
different 9-tap GF-FIR beamformers 10'. FIG. 27A shows the SNR-CR
design curves 2440, 2442, 2444, 2446 and 2448 for the 1-tap, 3-tap,
5-tap, 7-tap, and 9-tap GF-FIR beamformers 10', respectively, and
shows curve 2408 of the 9-tap DF-FIR beamformer 10 for comparison,
each with a receive focus of 1.0 cm and a design cyst radius of 0.4
mm. Note that design receive channel SNR (.sigma..sub.design.sup.2)
was varied from infinity to -40 dB. The GF-FIR design cures of FIG.
27A show similar trends as the DF-FIR design curves of FIG. 26A,
but it is noted that the 7-tap GF-FIR design curse 2446 allows for
slightly better performance than the 9-tap GF-FIR design curve 2408
at almost ever, design channel SNR value.
[0266] FIG. 27B shows the CR curves 2450, 2452, 2454, 2456 and 2458
as a function of receive channel SNR for the rectangular apodized
DAS 1000, SMF 1150, the optimal CR, optimal SNR and "knee" position
9-tap GF-FIR beamformers 10', respectively. The "knee" 9-tap GF-FIR
beamformer 10' offers almost a 20 dB gain in cystic resolution
compared to the conventional beamformer 10 as long as channel SNR
is greater than 20 Db, as can be seen by comparing curve 2460 with
curve 2450. As channel SNR worsens, the CR performance of the
"knee" 9-tap GF-FIR beamformer 10' decreases until it achieves
similar results to the DAS 10 and SMF beamformer 1150 around 0 dB
channel SNR, see curves 2460, 2450 and 2452.
[0267] FIG. 28 shows integrated lateral beamplots for the various
beamformers to illustrate how the sensitivity constrained QCLS
algorithm affects the ISR's of the GF FIR beamformer 10'. These
beamplots were made by integrating the energy of the individual
ISRs in range and then normalizing each to 0 dB. The optimal SNR
9-tap GF-FIR beamformer 10' (see plot 2600) has the widest mainlobe
2600M and highest sidelobes 2600S hence the decreased CR
performance according to the metric. The SMF beamformer 1150
lateral beamplot 2602 has a slightly narrower mainlobe 2602M and
lower sidelobes 2602S than the rectangular DAS beamplot 2604. The
beamplot for the 9-tap GF-FIR beamplot 2606 based on a selection at
the knee of the of the sigmoidal SNR-CR design curve and optimal CR
9-tap GF-FIR beamplot 2608 show dramatically reduced sidelobe
energy in the ISR as evidence by the sidelobe levels being much
lower than those of the other three curves.
[0268] With regard to the weights associated with the three
operating points for the 9-tap GF-FIR beamformer 10' (CR 2608, knee
2606 and SNR 2600, the temporal frequency of the filter taps 20T
increases as the beamformer selected moves from optimal SNR (e.g.,
see curve 2600) to optimal CR (e.g., see curve 2608). The optimal
SNR window functioned as a low pass filter, the optimal CR window
had high pass characteristics, and the "knee" window had bandpass
characteristics with the filter's center frequency slightly above
6.5 MHz. All filters had nonlinear phase characteristics and as the
comparison of the windows moved from optimal SNR to optimal CR the
phase response became more discontinuous across the aperture. The
frequency response differences between the "knee" and optimal CR
9-tap QCLS filters explained how the "knee" filters improved SNR
performance, as the knee filters kept more of the signal bandwidth
compared to the optimal CR filters.
[0269] A weighting function to the QCLS algorithm, as described
above, was also investigated. The weighting function used
emphasized ISR energy further away from the receive focus, hence,
the resulting weighted ISRs were expected to show faster sidelobe
rolloff compared to ISRs produced using FIR filters computed using
the QCLS algorithm without the weighting function. FIG. 29A shows
integrated lateral beamplots 2700, 2702, 2704, 2706 and 2708 for
rectangular apodized DAS beamformer 1000, SMF beamformer 1150, and
9-tap DF-FIR beamformer 10 as the weighting term assigned to ISR
energy further away from the focus increases (N=0, N=1, and N=2),
respectively. FIG. 29B shows cystic resolution cures 2710, 2712,
2714, 2716 and 2718 as a function of cyst radius for the
rectangular apodized DAS beamformer 10. SMF beamformer 1150, and
9-tap DF-FIR beamformer 10 for focuses of N=0, N=1, and N=2,
respectively. The figure shows how the cystic resolution
performance increases for larger cysts as the weighting term
assigned to ISR energy further away from the focus increases (N=0,
N=1, and N=2). The 9-lap WQCLS-FIR filters had a design cyst radius
of 0.4 mm and an infinite design SNR (optimal CR operating point).
It is interesting to note that the linearly weighted (N=2) 9-tap
WQCLS-FIR filters only reduced contrast by a few dB compared to the
unweighted 9-tap filters for the smaller cysts but offered a 15 dB
gain in cystic resolution at the larger cyst sizes. The
quadratically weighted (N=2) WQCLS-FIR filters suffered more for
the smaller cysts but achieved the best cystic resolution for cysts
larger than 3 mm in diameter. Large improvements were noted in all
of the curves for the 9-lap WQCLS FIR filters as compared to the
curves of the conventional DAS 1000 beamformer and the SMF
beamformer 1150. The integrated lateral beamplots of FIG. 29A show
how the weighting function can be used to decrease sidelobes for a
slight increase in mainlobe width. FIG. 29C shows the CR
performance as a function of channel SNR 2720, 2722, 2724, 2726 and
2728 for the five beamformer 1000, 1150, 10 (N=0), 10 (N=1) and 10
(N=2), respectively, at a constant cyst radius of 2.0 mm. Each
9-tap beamformer's cystic resolution performance begins to degrade
as the channel SNR approaches 70 dB. The quadratically weighted
9-tap WQCLS-FIR beamformer 10 outperforms the rectangular DAS
beamformer 1000 until channel SNR reaches 30 dB
Example 6
Performance of the Robust DF-FIR Beamformer in the Presence of
Phase Aberration
[0270] Example 2 above showed that aberrated non-robust FIR
beamformer 10 still improved contrast by 10 dB over the unaberrated
rectangular DAS beamformer 1000 for a large range of cyst sizes. In
this example, a similar analysis was conducted to investigate the
performance of the robust DF-FIR beamformer 10 in the presence of
aberration.
[0271] Recent literature indicates that phase aberrations in the
breast can be modeled as a nearfield thin phase screen
characterized by a root mean square (RMS) amplitude strength of 28
ns and a full-width at half-maximum (FWHM) correlation length of
3.6 mm, see Flax et al., "Phase aberration correction using signals
from point reflectors and diffuse scatterers: Basic Principles",
IEEE Transactions on Ultrasonics. Ferroelectrics and Frequency
Control. Vol. 35, pp 758-767, 1988 and Dahl et al., "Adaptive
imaging on a diagnostic ultrasound scanner at quasi real-time
rates". IEEE Transactions on Ultrasonics, Ferroelectrics and
Frequency Control, vol. 53, pp 1832-1843, 2006, both of which are
hereby incorporated herein, in their entireties, by reference
thereto. A nearfield phase screen aberrator was simulated to
distort the DF-FIR beamformer 10 ISR. Data from 150 realizations of
a one-dimensional aberrator were used to get good statistics. To
construct the aberrators, 150 random processes with an a priori 28
ns RMS strength and an a priori 3.6 mm FWHM correlation length were
generated. Each aberrator distorted the instant in time at which
each receive channel's spatial response was calculated. Note that
the same aberration would apply to all the ISRs required for the
input into the DF-FIR beamformer 10.
[0272] FIGS. 30A-30C show results of the aberration simulations
using three operating points for the 7-tap DF-FIR beamformer.
Cystic resolution curves (at infinite SNR) were plotted across a
range of cyst radii from 0.1 mm to 3.0 mm. Cystic resolution was
computed after centering the cyst about the peak of the aberrated
ISR for each beamformer. While this assumed spatial shift
invariance of the ISR over a small range, the cystic resolution
metric was applied consistently. From the 150 aberration
realizations, the mean and standard deviation of the cystic
resolution for each cyst size was calculated. From FIGS. 30A-30C,
it is clear that both the rectangular apodized DAS beamformer 1000
and 7-tap DF-FIR beamformer 10 experience degradation in cystic
resolution performance due to aberration. However, it appears that
all three 7-tap FIR beamformers 10 were relatively robust to phase
aberration as indicated by curves 2800, 2802 and 2804. The cystic
resolution performance for the "knee" and optimal CR 7-tap DF-FIR
beamformers (i.e., as shown by curves 2802 and 2804, respectively)
performed better in aberration than the unaberrated rectangular DAS
beam former 1000 (shown by curve 2806).
[0273] The performance of the weighted 7-tap QCLS filters was also
investigated: to determine whether relatively wider mainlobes would
be more robust to phase errors. The results from these simulations
are shown in FIGS. 31A-31C. Three sets of 7-tap WQCLS-FIR filters
for the DF-FIR beamformer were calculated. The first used a linear
spatial weighting function (N=1) and infinite design SNR (results
shown in FIG. 31A, aberrated 2900, unaberrated 2906), the second
used a quadratic spatial weighting function (N=2) and infinite
design SNR (results shown in FIG. 31B, aberrated 2902, unaberrated
2908), and the last one used a linear weighting function (N=1) and
the "knee" operating point of the design SNR-CR curve (results
shown in FIG. 31C, aberrated 2904. unaberrated 2910). Cystic
resolution was computed in the same manner as before. The
unaberrated optimal CR 7-tap DF-FIR cystic resolution curve 2808
was plotted for reference as well as the aberrated and unaberrated
rectangular DAS cures 2810 and 2806, respectively. These results
show that the spatial weighting function can be used to design FIR
beamformers that are more robust in the presence of tissue induced
aberration than the unweighted, optimal CR FIR beamformer (i.e.,
compare results of each of 2900, 2902 and 2904 to 2808).
Example 7
Comparison of DSIQ and FIR-DSIQ Beamforming
[0274] Computer simulations were performed to assess the
performance improvements possible by incorporating the FIR
apodization scheme of the present invention in concert with DSIQ
beamforming. A conventional one-dimensional linear array transducer
was simulated and PSFs were computed for both double cycle and
transmission seven cycle transmission. This variation was chosen to
explore the role of bandwidth in DSIQ-FIR performance. This is of
particular interest as DSIQ beamforming is known to perform better
when lower bandwidth (more transmit cycles) is used. FIR filter
coefficients were designed for both the broadband and narrowband
cases and for a cyst diameter of 350 microns. Note that the FIR
filter coefficients were not designed using the robust methodology
and thus yield some loss in sensitivity.
[0275] Simulation results are shown, in FIG. 32. The 2-cycle DSIQ
beamplot 3203 is the broadest and has the highest sidelobe levels.
This is a very poor quality beamplot and would be expected to yield
particularly poor image quality. The 7-cycle DSIQ beamplot 3200 has
a significantly narrower mainlobe, but still exhibits a high
sidelobe level. The 7-cycle DSIQ-FIR beamplot 3204 maintains the
narrow mainlobe of the 7-cycle DSIQ beamformer, but lowers the
sidelobe levels by roughly 10 dB. This is a dramatic improvement
that would be expected to notably improve image contrast. Finally,
the 2-cycle DSIQ-FIR beamplot 3206 shows a narrow mainlobe with
sidelobes well below those seen for any other beamformer. These
results indicate that the combination of FIR apodization with DSIQ
beamforming improves imaging performance under all conditions, and
enables the DSIQ beamformer to operated within broadband signals.
This is particularly important as the conventional DSIQ beamformer
cannot operate effectively with narrowband signals.
[0276] While the present invention has been described with
reference to the specific embodiments thereof, it should be
understood by those skilled in the art that various changes may be
made and equivalents may be substituted without departing from the
true spirit and scope of the invention. In addition, many
modifications may be made to adapt a particular situation,
material, composition of matter, process, process step or steps, to
the objective, spirit and scope of the present invention. All such
modifications are intended to be within the scope of the claims
appended hereto.
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